@string{aistats8 = {8th International Conference on Artificial Intelligence and Statistics}} @string{aistats9 = {9th International Conference on Artificial Intelligence and Statistics}} @string{aistats10 = {10th International Conference on Artificial Intelligence and Statistics}} @string{aistats11 = {11th International Conference on Artificial Intelligence and Statistics}} @string{aistats12 = {12th International Conference on Artificial Intelligence and Statistics}} @string{aistats13 = {13th International Conference on Artificial Intelligence and Statistics}} @string{aistats14 = {14th International Conference on Artificial Intelligence and Statistics}} @string{icml20 = {20th International Conference on Machine Learning}} @string{icml21 = {21st International Conference on Machine Learning}} @string{icml22 = {22nd International Conference on Machine Learning}} @string{icml23 = {23rd International Conference on Machine Learning}} @string{icml24 = {24th International Conference on Machine Learning}} @string{icml25 = {25th International Conference on Machine Learning}} @string{icml26 = {26th International Conference on Machine Learning}} @string{icml27 = {27th International Conference on Machine Learning}} @string{icml28 = {28th International Conference on Machine Learning}} @string{nips8 = {Advances in Neural Information Processing Systems 8}} @string{nips9 = {Advances in Neural Information Processing Systems 9}} @string{nips10 = {Advances in Neural Information Processing Systems 10}} @string{nips11 = {Advances in Neural Information Processing Systems 11}} @string{nips12 = {Advances in Neural Information Processing Systems 12}} @string{nips13 = {Advances in Neural Information Processing Systems 13}} @string{nips14 = {Advances in Neural Information Processing Systems 14}} @string{nips15 = {Advances in Neural Information Processing Systems 15}} @string{nips16 = {Advances in Neural Information Processing Systems 16}} @string{nips17 = {Advances in Neural Information Processing Systems 17}} @string{nips18 = {Advances in Neural Information Processing Systems 18}} @string{nips19 = {Advances in Neural Information Processing Systems 19}} @string{nips20 = {Advances in Neural Information Processing Systems 20}} @string{nips21 = {Advances in Neural Information Processing Systems 21}} @string{nips22 = {Advances in Neural Information Processing Systems 22}} @string{nips23 = {Advances in Neural Information Processing Systems 23}} @string{nips24 = {Advances in Neural Information Processing Systems 24}} @string{nips25 = {Advances in Neural Information Processing Systems 25}} @string{cogsci32 = {The Proceedings of the 32nd Annual Meeting of the Cognitive Science Society}} @String{uai22 = {22nd Conference on Uncertainty in Artificial Intelligence}} @String{uai27 = {27nd Conference on Uncertainty in Artificial Intelligence}} @string{cup = {Cambridge University Press}} @string{AAAI = {AAAI Press}} @string{mit = {The {MIT} Press}} @string{oup = {Oxford University Press}} @string{WILEY = {John Wiley \& Sons}} @String{rss9 = {9th International Conference on Robotics: Science \& Systems}} @string{IECY = {IEEE Transactions on System Science and Cybernetics}} @string{IENN = {IEEE Transactions on Neural Networks}} @string{PAMI = {IEEE Transactions on Pattern Analysis and Machine Intelligence}} @string{tcbb = {IEEE/ACM Transactions on Computational Biology and Bioinformatics}} @string{jasa = {Journal of the Americal Statistical Association}} @string{jmlr = {Journal of Machine Learning Research}} @string{jrssB = {Journal of the Royal Statistical Society, Series B}} @string{jcst = {Journal of Computer Science and Technology}} @string{nc = {Neural Computation}} @string{PCPS = {Proceedings of the Cambridge Philosophical Society}} @string{tams = {The Annals of Mathematical Statistics}} @string{lncs = {Lecture Notes in Computer Science (LNCS)}} @inproceedings{Roy11, cat = {np gm}, author = {Daniel M. Roy}, title = {On the computability and complexity of Bayesian reasoning}, booktitle = {NIPS Workshop on Philosophy and Machine Learning}, year = 2011, url = {http://danroy.org/papers/Roy-NIPSPML-2011.pdf}, abstract = { If we consider the claim made by some cognitive scientists that the mind performs Bayesian reasoning, and if we simultaneously accept the Physical Church-Turing thesis and thus believe that the computational power of the mind is no more than that of a Turing machine, then what limitations are there to the reasoning abilities of the mind? I give an overview of joint work with Nathanael Ackerman (Harvard, Mathematics) and Cameron Freer (MIT, CSAIL) that bears on the computability and complexity of Bayesian reasoning. In particular, we prove that conditional probability is in general not computable in the presence of continuous random variables. However, in light of additional structure in the prior distribution, such as the presence of certain types of noise, or of exchangeability, conditioning is possible. These results cover most of statistical practice. At the workshop on Logic and Computational Complexity, we presented results on the computational complexity of conditioning, embedding sharp-P-complete problems in the task of computing conditional probabilities for diffuse continuous random variables. This work complements older work. For example, under cryptographic assumptions, the computational complexity of producing samples and computing probabilities was separated by Ben-David, Chor, Goldreich and Luby. In recent work, we also make use of cryptographic assumptions to show that different representations of exchangeable sequences may have vastly different complexity. However, when faced with an adversary that is computational bounded, these different representations have the same complexity, highlighting the fact that knowledge representation and approximation play a fundamental role in the possibility and plausibility of Bayesian reasoning.} } @inproceedings{SonRoy11, cat = {approx}, author = {David Sontag and Daniel M. Roy}, title = {The {C}omplexity of {I}nference in {L}atent {D}irichlet {A}llocation}, booktitle = nips24, year = 2011, address = {Cambridge, MA, USA}, publisher = mit, url = {http://danroy.org/papers/SonRoy-NIPS-2011.pdf}, abstract = { We consider the computational complexity of probabilistic inference in Latent Dirichlet Allocation (LDA). First, we study the problem of finding the maximum a posteriori (MAP) assignment of topics to words, where the document's topic distribution is integrated out. We show that, when the effective number of topics per document is small, exact inference takes polynomial time. In contrast, we show that, when a document has a large number of topics, finding the MAP assignment of topics to words in LDA is NP-hard. Next, we consider the problem of finding the MAP topic distribution for a document, where the topic-word assignments are integrated out. We show that this problem is also NP-hard. Finally, we briefly discuss the problem of sampling from the posterior, showing that this is NP-hard in one restricted setting, but leaving open the general question. } } @inproceedings{AbbHelGrietal11, cat = {clust}, author = {Joshua Abbott and Katherine A. Heller and Zoubin Ghahramani and Thomas L. Griffiths}, title = {Testing a {Bayesian} Measure of Representativeness Using a Large Image Database}, booktitle = nips24, year = 2011, address = {Cambridge, MA, USA}, publisher = mit, url = {.}, abstract = {How do people determine which elements of a set are most representative of that set? We extend an existing Bayesian measure of representativeness, which indicates the representativeness of a sample from a distribution, to define a measure of the representativeness of an item to a set. We show that this measure is formally related to a machine learning method known as Bayesian Sets. Building on this connection, we derive an analytic expression for the representativeness of objects described by a sparse vector of binary features. We then apply this measure to a large database of images, using it to determine which images are the most representative members of different sets. Comparing the resulting predictions to human judgments of representativeness provides a test of this measure with naturalistic stimuli, and illustrates how databases that are more commonly used in computer vision and machine learning can be used to evaluate psychological theories.} } @inproceedings{AdaGha09, cat = {ssl np gp}, booktitle = icml26, title = {Archipelago: nonparametric {B}ayesian semi-supervised learning}, author = {R.~Adams and Zoubin Ghahramani}, year = 2009, address = {Montr\'{e}al, QC, Canada}, month = {June}, publisher = {Omnipress}, pages = {1--8}, editor = {L\'{e}on Bottou and Michael Littman}, url = {.}, abstract = {Semi-supervised learning (SSL), is classification where additional unlabeled data can be used to improve accuracy. Generative approaches are appealing in this situation, as a model of the data's probability density can assist in identifying clusters. Nonparametric Bayesian methods, while ideal in theory due to their principled motivations, have been difficult to apply to SSL in practice. We present a nonparametric Bayesian method that uses Gaussian processes for the generative model, avoiding many of the problems associated with Dirichlet process mixture models. Our model is fully generative and we take advantage of recent advances in Markov chain Monte Carlo algorithms to provide a practical inference method. Our method compares favorably to competing approaches on synthetic and real-world multi-class data.}, annote = {This paper was awarded Honourable Mention for Best Paper at ICML 2009.} } @inproceedings{AdaGhaJor10, cat = {np clust}, author = {Ryan P. Adams and Zoubin Ghahramani and Michael I. Jordan}, year = 2010, title = {Tree-Structured Stick Breaking for Hierarchical Data}, booktitle = nips23, publisher = mit, url = {.}, abstract = {Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data. } } @inproceedings{AdaWalGha10, cat = {np gm}, author = {R.~P.~Adams and H.~Wallach and Zoubin Ghahramani}, year = 2010, month = {May}, editor = {Yee Whye Teh and Mike Titterington}, title = {Learning the Structure of Deep Sparse Graphical Models}, booktitle = aistats13, address = {Chia Laguna, Sardinia, Italy}, pages = {1--8}, url = {.}, abstract = {Deep belief networks are a powerful way to model complex probability distributions. However, it is difficult to learn the structure of a belief network, particularly one with hidden units. The Indian buffet process has been used as a nonparametric Bayesian prior on the structure of a directed belief network with a single infinitely wide hidden layer. Here, we introduce the cascading Indian buffet process (CIBP), which provides a prior on the structure of a layered, directed belief network that is unbounded in both depth and width, yet allows tractable inference. We use the CIBP prior with the nonlinear Gaussian belief network framework to allow each unit to vary its behavior between discrete and continuous representations. We use Markov chain Monte Carlo for inference in this model and explore the structures learned on image data.}, annote = {Winner of the Best Paper Award} } @article{AndSzyRasetal02, cat = {gp}, author = {Irene K.~Andersen and Anna Szymkowiak and Carl Edward Rasmussen and L.~G.~Hanson and J.~R.~Marstrand and H.~B.~W.~Larsson and Lars Kai Hansen}, title = {Perfusion Quantification using {G}aussian Process Deconvolution}, url = {.}, doi = {10.1002/mrm.10213}, journal = {Magnetic Resonance in Medicine}, volume = 48, number = 2, pages = {351--361}, year = 2002, abstract = {The quantification of perfusion using dynamic susceptibility contrast MR imaging requires deconvolution to obtain the residual impulse-response function (IRF). Here, a method using a Gaussian process for deconvolution, GPD, is proposed. The fact that the IRF is smooth is incorporated as a constraint in the method. The GPD method, which automatically estimates the noise level in each voxel, has the advantage that model parameters are optimized automatically. The GPD is compared to singular value decomposition (SVD) using a common threshold for the singular values and to SVD using a threshold optimized according to the noise level in each voxel. The comparison is carried out using artificial data as well as using data from healthy volunteers. It is shown that GPD is comparable to SVD variable optimized threshold when determining the maximum of the IRF, which is directly related to the perfusion. GPD provides a better estimate of the entire IRF. As the signal to noise ratio increases or the time resolution of the measurements increases, GPD is shown to be superior to SVD. This is also found for large distribution volumes.} } @inproceedings{ArnSchLar09, title = {Bayesian nonnegative matrix factorization with volume prior for unmixing of hyperspectral images}, author = {Morten Arngren and Mikkel N.~Schmidt and Jan Larsen}, booktitle = {Machine Learning for Signal Processing, IEEE Workshop on (MLSP)}, address = {Grenoble, France}, month = {September}, pages = {1--6}, year = 2009, isbn = {978-1-4244-4947-7}, doi = {10.1109/MLSP.2009.5306262}, url = {.}, abstract = {In hyperspectral image analysis the objective is to unmix a set of acquired pixels into pure spectral signatures (endmembers) and corresponding fractional abundances. The Non-negative Matrix Factorization (NMF) methods have received a lot of attention for this unmixing process. Many of these NMF based unmixing algorithms are based on sparsity regularization encouraging pure spectral endmembers, but this is not optimal for certain applications, such as foods, where abundances are not sparse. The pixels will theoretically lie on a simplex and hence the endmembers can be estimated as the vertices of the smallest enclosing simplex. In this context we present a Bayesian framework employing a volume constraint for the NMF algorithm, where the posterior distribution is numerically sampled from using a Gibbs sampling procedure. We evaluate the method on synthetical and real hyperspectral data of wheat kernels.}, annote = {This paper was "rated among the best papers submitted" to the 2009 Machine Learning for Signal Processing conference.} } @inproceedings{Azr07, cat = {ssl}, author = {Arik Azran}, title = {The {R}endezvous algorithm: multiclass semi-supervised learning with {M}arkov random walks}, booktitle = icml24, address = {Corvallis, OR, USA}, editor = {Zoubin Ghahramani}, publisher = {Omnipress}, year = 2007, month = {June}, pages = {49--56}, url = {.}, abstract = {We consider the problem of multiclass classification where both labeled and unlabeled data points are given. We introduce and demonstrate a new approach for estimating a distribution over the missing labels where data points are viewed as nodes of a graph, and pairwise similarities are used to derive a transition probability matrix P for a Markov random walk between them. The algorithm associates each point with a particle which moves between points according to P. Labeled points are set to be absorbing states of the Markov random walk, and the probability of each particle to be absorbed by the different labeled points, as the number of steps increases, is then used to derive a distribution over the associated missing label. A computationally efficient algorithm to implement this is derived and demonstrated on both real and artificial data sets, including a numerical comparison with other methods.} } @inproceedings{AzrGha06, author = {Arik Azran and Zoubin Ghahramani}, title = {A new approach to data driven clustering}, booktitle = icml23, publisher = {Omnipress}, editor = {William Cohen and Andrew Moore}, address = {Pittsburgh, PA, USA}, pages = {57--64}, year = 2006, month = {June}, url = {.}, abstract = {We consider the problem of clustering in its most basic form where only a local metric on the data space is given. No parametric statistical model is assumed, and the number of clusters is learned from the data. We introduce, analyze and demonstrate a novel approach to clustering where data points are viewed as nodes of a graph, and pairwise similarities are used to derive a transition probability matrix P for a Markov random walk between them. The algorithm automatically reveals structure at increasing scales by varying the number of steps taken by this random walk. Points are represented as rows of Pt, which are the t-step distributions of the walk starting at that point; these distributions are then clustered using a KL-minimizing iterative algorithm. Both the number of clusters, and the number of steps that best reveal it, are found by optimizing spectral properties of P.} } @inproceedings{AzrGha06b, author = {Arik Azran and Zoubin Ghahramani}, title = {Spectral Methods for Automatic Multiscale Data Clustering}, booktitle = {IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}, year = 2006, month = {June}, address = {New York, NY, USA}, publisher = {IEEE Computer Society}, isbn = {0-7695-2597-0}, pages = {190--197}, doi = {10.1109/CVPR.2006.289}, url = {.}, abstract = {Spectral clustering is a simple yet powerful method for finding structure in data using spectral properties of an associated pairwise similarity matrix. This paper provides new insights into how the method works and uses these to derive new algorithms which given the data alone automatically learn different plausible data partitionings. The main theoretical contribution is a generalization of a key result in the field, the multicut lemma (Meila 2001). We use this generalization to derive two algorithms. The first uses the eigenvalues of a given affinity matrix to infer the number of clusters in data, and the second combines learning the affinity matrix with inferring the number of clusters. A hierarchical implementation of the algorithms is also derived. The algorithms are theoretically motivated and demonstrated on nontrivial data sets.} } @inproceedings{BeaGhaRas02, cat = {np}, author = {Matthew J.~Beal and Zoubin Ghahramani and Carl Edward Rasmussen}, title = {The Infinite Hidden {M}arkov Model}, booktitle = nips14, pages = {577--584}, editors = {T. Dietterich, S. Becker, Z. Ghahramani}, address = {Cambridge, MA, USA}, publisher = mit, year = 2002, month = {December}, url = {.}, abstract = {We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying state-transition matrix, and the expected number of distinct hidden states in a finite sequence. In this framework it is also natural to allow the alphabet of emitted symbols to be infinite --- consider, for example, symbols being possible words appearing in English text.} } @inproceedings{BraOrt10, cat = {rl}, author = {Daniel A.~Braun and Pedro A.~Ortega}, title = {A minimum relative entropy principle for adaptive control in linear quadratic regulators}, booktitle = {Proceedings of the 7th international conference on informatics in control, automation and robotics}, pages = {(in press)}, year = 2010, url = {.}, abstract = {The design of optimal adaptive controllers is usually based on heuristics, because solving Bellman's equations over information states is notoriously intractable. Approximate adaptive controllers often rely on the principle of certainty-equivalence where the control process deals with parameter point estimates as if they represented ``true'' parameter values. Here we present a stochastic control rule instead where controls are sampled from a posterior distribution over a set of probabilistic input-output models and the true model is identified by Bayesian inference. This allows reformulating the adaptive control problem as an inference and sampling problem derived from a minimum relative entropy principle. Importantly, inference and action sampling both work forward in time and hence such a Bayesian adaptive controller is applicable on-line. We demonstrate the improved performance that can be achieved by such an approach for linear quadratic regulator examples.} } @inproceedings{BraOrtTheSch11, cat = {rl}, author = {Daniel A.~Braun and Pedro A.~Ortega and Evangelos Theodorou and Stefan Schaal}, title = {Path Integral Control and Bounded Rationality}, booktitle = {2011 {IEEE} Symposium on Adaptive Dynamic Programming and Reinforcement Learning}, year = 2011, url = {.}, abstract = {Path integral methods have recently been shown to be applicable to a very general class of optimal control problems. Here we examine the path integral formalism from a decision-theoretic point of view, since an optimal controller can always be regarded as an instance of a perfectly rational decision-maker that chooses its actions so as to maximize its expected utility. The problem with perfect rationality is, however, that finding optimal actions is often very difficult due to prohibitive computational resource costs that are not taken into account. In contrast, a bounded rational decision-maker has only limited resources and therefore needs to strike some compromise between the desired utility and the required resource costs. In particular, we suggest an information-theoretic measure of resource costs that can be derived axiomatically. As a consequence we obtain a variational principle for choice probabilities that trades off maximizing a given utility criterion and avoiding resource costs that arise due to deviating from initially given default choice probabilities. The resulting bounded rational policies are in general probabilistic. We show that the solutions found by the path integral formalism are such bounded rational policies. Furthermore, we show that the same formalism generalizes to discrete control problems, leading to linearly solvable bounded rational control policies in the case of Markov systems. Importantly, Bellman's optimality principle is not presupposed by this variational principle, but it can be derived as a limit case. This suggests that the information theoretic formalization of bounded rationality might serve as a general principle in control design that unifies a number of recently reported approximate optimal control methods both in the continuous and discrete domain.}, } @article{BraOrtWol11, author = {Daniel A. Braun and Pedro A. Ortega and Daniel M. Wolpert}, title = {Motor coordination: When two have to act as one}, journal = {Special issue of Experimental Brain Research on Joint Action}, year = 2011, abstract = {Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as "choosing sides", "stag hunt", "chicken", and "battle of sexes". In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players' movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players' responses. Moreover, we found that the probability of successful coordination depends on the players' initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.}, url = {http://www.ncbi.nlm.nih.gov/pubmed/21455618} } @article{BraOrtWol11b, author = {Daniel A.~Braun and Pedro A.~Ortega and Daniel M.~Wolpert}, title = {Nash equilibria in multi-agent motor interactions}, journal = {PLoS Computational Biology}, year = 2009, volume = 5, number = 8, abstract = {Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.}, url = {http://www.ncbi.nlm.nih.gov/pubmed/19680426} } @inproceedings{BraVanVlaGha10, cat = {np mcmc}, author = {S\'{e}bastien Brati\`{e}res and Jurgen {Van Gael} and Andreas Vlachos and Zoubin Ghahramani}, abstract = {This paper compares parallel and distributed implementations of an iterative, Gibbs sampling, machine learning algorithm. Distributed implementations run under Hadoop on facility computing clouds. The probabilistic model under study is the infinite HMM [1], in which parameters are learnt using an instance blocked Gibbs sampling, with a step consisting of a dynamic program. We apply this model to learn part-of-speech tags from newswire text in an unsupervised fashion. However our focus here is on runtime performance, as opposed to NLP-relevant scores, embodied by iteration duration, ease of development, deployment and debugging.}, address = {Bradford, UK}, booktitle = {Proceedings of the 2010 10th IEEE International Conference on Computer and Information Technology}, pages = {1235--1240}, title = {Scaling the {iHMM}: {P}arallelization versus {H}adoop}, url = {.}, year = 2010, isbn = {978-0-7695-4108-2}, doi = {10.1109/CIT.2010.223}, publisher = {IEEE Computer Society} } @article{ChaCunGlo09, cat = {gp}, author = {C. Chang and J. P. Cunningham and G. Glover}, title = {Influence of heart rate on the BOLD signal: the cardiac response function}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/ChangNeuroimage2009.pdf}, journal = {NeuroImage}, volume = 44, pages = {857-869}, year = 2009, abstract = {It has previously been shown that low-frequency fluctuations in both respiratory volume and cardiac rate can induce changes in the blood-oxygen level dependent (BOLD) signal. Such physiological noise can obscure the detection of neural activation using fMRI, and it is therefore important to model and remove the effects of this noise. While a hemodynamic response function relating respiratory variation (RV) and the BOLD signal has been described, no such mapping for heart rate (HR) has been proposed. In the current study, the effects of RV and HR are simultaneously deconvolved from resting state fMRI. It is demonstrated that a convolution model including RV and HR can explain significantly more variance in gray matter BOLD signal than a model that includes RV alone, and an average HR response function is proposed that well characterizes our subject population. It is observed that the voxel-wise morphology of the deconvolved RV responses is preserved when HR is included in the model, and that its form is adequately modeled by Birn et al.'s previously described respiration response function. Furthermore, it is shown that modeling out RV and HR can significantly alter functional connectivity maps of the default-mode network.} } @article{ChuCunKauetal10, author = {M. M. Churchland and J. P. Cunningham and M. T. Kaufman and S. I. Ryu and K. V. Shenoy.}, title = {Cortical preparatory activity: Representation of movement or first cog in a dynamical machine?}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/ChurchlandNeuron2010.pdf}, journal = {Neuron}, volume = 68, pages = {387-400}, year = 2010, abstract = {The motor cortices are active during both movement and movement preparation. A common assumption is that preparatory activity constitutes a subthreshold form of movement activity: a neuron active during rightward movements becomes modestly active during preparation of a rightward movement. We asked whether this pattern of activity is, in fact, observed. We found that it was not: at the level of a single neuron, preparatory tuning was weakly correlated with movement-period tuning. Yet, somewhat paradoxically, preparatory tuning could be captured by a preferred direction in an abstract "space" that described the population-level pattern of movement activity. In fact, this relationship accounted for preparatory responses better than did traditional tuning models. These results are expected if preparatory activity provides the initial state of a dynamical system whose evolution produces movement activity. Our results thus suggest that preparatory activity may not represent specific factors, and may instead play a more mechanistic role.} } @inproceedings{ChuGha09, volume = 5, author = {W. Chu and Z. Ghahramani}, note = {ISSN 1938-7228}, booktitle = aistats12, editor = {D. van Dyk and M. Welling}, title = {Probabilistic models for incomplete multi-dimensional arrays}, address = {Clearwater Beach, FL, USA}, publisher = {Microtome Publishing (paper) Journal of Machine Learning Research}, year = 2009, month = {April}, pages = {89--96}, url = {.}, abstract = {In multiway data, each sample is measured by multiple sets of correlated attributes. We develop a probabilistic framework for modeling structural dependency from partially observed multi-dimensional array data, known as pTucker. Latent components associated with individual array dimensions are jointly retrieved while the core tensor is integrated out. The resulting algorithm is capable of handling large-scale data sets. We verify the usefulness of this approach by comparing against classical models on applications to modeling amino acid fluorescence, collaborative filtering and a number of benchmark multiway array data.} } @inproceedings{ChuSinGhaetal07, cat = {gp}, volume = 19, month = {September}, author = {W. Chu and V. Sindhwani and Z. Ghahramani and S. Keerthi}, series = {Bradford Books}, note = {Online contents gives pages 314--321, and 289--296 on pdf of contents}, booktitle = nips19, editor = {B. Sch\"olkopf and J. Platt and T. Hofmann}, title = {Relational learning with {G}aussian processes}, address = {Cambridge, MA, USA}, publisher = mit, year = 2007, pages = {289--296}, url = {.}, abstract = {Correlation between instances is often modelled via a kernel function using input attributes of the instances. Relational knowledge can further reveal additional pairwise correlations between variables of interest. In this paper, we develop a class of models which incorporates both reciprocal relational information and input attributes using Gaussian process techniques. This approach provides a novel non-parametric Bayesian framework with a data-dependent prior for supervised learning tasks. We also apply this framework to semi-supervised learning. Experimental results on several real world data sets verify the usefulness of this algorithm.} } @article{ChuYuCunetal10, cat = {gp}, author = {M. M. Churchland and B. M. Yu and J. P. Cunningham and L. P. Sugrue and M. R. Cohen and G. S. Corrado and W. T. Newsome and A. M. Clark and P. Hosseini and B. B. Scott and D. C. Bradley and M. A. Smith and A. Kohn and J. A. Movshon and K. M. Armstrong and T. Moore and S. W. Chang and L. H. Snyder and S. G. Lisberger and N. J. Priebe and I. M. Finn and D. Ferster and S. I. Ryu and G. Santhanam and M. Sahani and K. V. Shenoy.}, title = {Stimulus onset quashes neural variability: a widespread cortical phenomenon}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/ChurchlandNN2010.pdf}, journal = {Nature Neuroscience}, volume = 13, pages = {369-378}, year = 2010, abstract = {Neural responses are typically characterized by computing the mean firing rate, but response variability can exist across trials. Many studies have examined the effect of a stimulus on the mean response, but few have examined the effect on response variability. We measured neural variability in 13 extracellularly recorded datasets and one intracellularly recorded dataset from seven areas spanning the four cortical lobes in monkeys and cats. In every case, stimulus onset caused a decline in neural variability. This occurred even when the stimulus produced little change in mean firing rate. The variability decline was observed in membrane potential recordings, in the spiking of individual neurons and in correlated spiking variability measured with implanted 96-electrode arrays. The variability decline was observed for all stimuli tested, regardless of whether the animal was awake, behaving or anaesthetized. This widespread variability decline suggests a rather general property of cortex, that its state is stabilized by an input.} } @techreport{Cun08, cat = {gp approx}, title = {Derivation of {E}xpectation {P}ropagation for "Fast {G}aussian process methods for point process intensity estimation"}, author = {J. P. Cunningham}, year = 2008, institution = {Stanford University}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/CunninghamEPTR2008.pdf}, abstract = {We derive the Expectation Propagation algorithm updates for approximating the posterior distribution on intensity in a conditionally inhomogeneous gamma interval process with a Gaussian Process prior (GP IGIP), a model which appeared in Cunningham, Shenoy, Sahani (2008) ICML.} } @article{CunNuyGiletal11, cat = {time}, author = {J. P. Cunningham and P. Nuyujukian and V. Gilja and C. A. Chestek and S. I. Ryu and K. V. Shenoy.}, title = {A closed-loop human simulator for investigating the role of feedback-control in brain-machine interfaces}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/CunninghamJNP2011.pdf}, journal = {Journal of Neurophysiology}, volume = 105, pages = {1932-1949}, year = 2011, abstract = {Neural prosthetic systems seek to improve the lives of severely disabled people by decoding neural activity into useful behavioral commands. These systems and their decoding algorithms are typically developed "offline", using neural activity previously gathered from a healthy animal, and the decoded movement is then compared with the true movement that accompanied the recorded neural activity. However, this offline design and testing may neglect important features of a real prosthesis, most notably the critical role of feedback control, which enables the user to adjust neural activity while using the prosthesis. We hypothesize that under- standing and optimally designing high-performance decoders require an experimental platform where humans are in closed-loop with the various candidate decode systems and algorithms. It remains unexplored the extent to which the subject can, for a particular decode system, algorithm, or parameter, engage feedback and other strategies to improve decode performance. Closed-loop testing may suggest different choices than offline analyses. Here we ask if a healthy human subject, using a closed-loop neural prosthesis driven by synthetic neural activity, can inform system design. We use this online pros- thesis simulator (OPS) to optimize "online" decode performance based on a key parameter of a current state-of-the-art decode algorithm, the bin width of a Kalman filter. First, we show that offline and online analyses indeed suggest different parameter choices. Previous literature and our offline analyses agree that neural activity should be analyzed in bins of 100- to 300-ms width. OPS analysis, which incorporates feedback control, suggests that much shorter bin widths (25-50 ms) yield higher decode performance. Second, we confirm this surprising finding using a closed-loop rhesus monkey prosthetic system. These findings illustrate the type of discovery made possible by the OPS, and so we hypothesize that this novel testing approach will help in the design of prosthetic systems that will translate well to human patients.} } @inproceedings{CunSheSah08, cat = {gp}, author = {J. P. Cunningham and K. V. Shenoy and M. Sahani}, booktitle = icml25, title = {Fast {G}aussian process methods for point process intensity estimation}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/CunninghamICML2008.pdf}, year = 2008, address = {Helsinki, Finland}, month = {June}, pages = {1--8}, abstract = {Point processes are difficult to analyze because they provide only a sparse and noisy observation of the intensity function driving the process. Gaussian Processes offer an attractive framework within which to infer underlying intensity functions. The result of this inference is a continuous function defined across time that is typically more amenable to analytical efforts. However, a naive implementation will become computationally infeasible in any problem of reasonable size, both in memory and run time requirements. We demonstrate problem specific methods for a class of renewal processes that eliminate the memory burden and reduce the solve time by orders of magnitude.} } @inproceedings{CunYuSheetal08, cat = {gp}, author = {J. P. Cunningham and B. M. Yu and K. V. Shenoy and M. Sahani}, booktitle = nips20, title = {Inferring neural firing rates from spike trains using {G}aussian processes}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/CunninghamNIPS2008.pdf}, year = 2008, address = {Vancouver, BC}, month = {December}, pages = {1--8}, abstract = {Neural spike trains present challenges to analytical efforts due to their noisy, spiking nature. Many studies of neuroscientific and neural prosthetic importance rely on a smoothed, denoised estimate of the spike train's underlying firing rate. Current techniques to find time-varying firing rates require ad hoc choices of parameters, offer no confidence intervals on their estimates, and can obscure potentially important single trial variability. We present a new method, based on a Gaussian Process prior, for inferring probabilistically optimal estimates of firing rate functions underlying single or multiple neural spike trains. We test the performance of the method on simulated data and experimentally gathered neural spike trains, and we demonstrate improvements over conventional estimators.}, annote = {Spotlight Presentation} } @inproceedings{DavGha11, month = {August}, author = {Davies, A. and Ghahramani, Z.}, title = {Language-independent {B}ayesian sentiment mining of Twitter}, year = 2011, booktitle = {In {\em The Fifth Workshop on Social Network Mining and Analysis (SNA-KDD 2011)}}, url = {http://www.alexdavies.net/wordpress/wp-content/uploads/2011/09/Language-Indepedent-Bayesian-Sentiment-Mining-of-Twitter.pdf}, abstract = {This paper outlines a new language-independent model for sentiment analysis of short, social-network statuses. We demonstrate this on data from Twitter, modelling happy vs sad sentiment, and show that in some circumstances this outperforms similar Naive Bayes models by more than 10\%. We also propose an extension to allow the modelling of differ- ent sentiment distributions in different geographic regions, while incorporating information from neighbouring regions. We outline the considerations when creating a system analysing Twitter data and present a scalable system of data acquisi- tion and prediction that can monitor the sentiment of tweets in real time.} } @inproceedings{DeiHubHan09, cat = {gp time}, author = {Marc Peter Deisenroth and Marco F. Huber and Uwe D. Hanebeck}, title = {Analytic Moment-based {G}aussian Process Filtering}, booktitle = icml26, year = 2009, editor = {L\'{e}on Bottou and Michael Littman}, pages = {225--232}, address = {Montr\'{e}al, QC, Canada}, month = {June}, publisher = {Omnipress}, url = {.}, abstract = {We propose an analytic moment-based filter for nonlinear stochastic dynamic systems modeled by Gaussian processes. Exact expressions for the expected value and the covariance matrix are provided for both the prediction step and the filter step, where an additional Gaussian assumption is exploited in the latter case. Our filter does not require further approximations. In particular, it avoids finite-sample approximations. We compare the filter to a variety of Gaussian filters, that is, the EKF, the UKF, and the recent GP-UKF proposed by Ko et al. (2007).}, annote = {With corrections. code.} } @inproceedings{DeiPetRas08, cat = {gp approx}, author = {Marc Peter Deisenroth and Jan Peters and Carl Edward Rasmussen}, title = {Approximate Dynamic Programming with {G}aussian Processes}, booktitle = {2008 American Control Conference (ACC 2008)}, year = 2008, pages = {4480--4485}, address = {Seattle, WA, USA}, month = {June}, url = {.}, abstract = {In general, it is difficult to determine an optimal closed-loop policy in nonlinear control problems with continuous-valued state and control domains. Hence, approximations are often inevitable. The standard method of discretizing states and controls suffers from the curse of dimensionality and strongly depends on the chosen temporal sampling rate. The paper introduces Gaussian Process Dynamic Programming (GPDP). In GPDP, value functions in the Bellman recursion of the dynamic programming algorithm are modeled using Gaussian processes. GPDP returns an optimal state-feedback for a finite set of states. Based on these outcomes, we learn a possibly discontinuous closed-loop policy on the entire state space by switching between two independently trained Gaussian processes.}, annote = {code.} } @inproceedings{DeiRas09, cat = {rl}, author = {Marc Peter Deisenroth and Carl Edward Rasmussen}, title = {Bayesian Inference for Efficient Learning in Control}, booktitle = {Multidisciplinary Symposium on Reinforcement Learning}, year = 2009, address = {Montr\'{e}al, QC, Canada}, month = {June}, url = {.}, abstract = {In contrast to humans or animals, artificial learners often require more trials when learning motor control tasks solely based on experience. Efficient autonomous learners will reduce the amount of engineering required to solve control problems. By using probabilistic forward models, we can employ two key ingredients of biological learning systems to speed up artificial learning. We present a consistent and coherent Bayesian framework that allows for efficient autonomous experience-based learning. We demonstrate the success of our learning algorithm by applying it to challenging nonlinear control problems in simulation and in hardware.} } @inproceedings{DeiRas09b, cat = {rl}, author = {Marc Peter Deisenroth and Carl Edward Rasmussen}, title = {Efficient Reinforcement Learning for Motor Control}, booktitle = {10th International PhD Workshop on Systems and Control}, year = 2009, address = {Hlubok\'{a} nad Vltavou, Czech Republic}, month = {September}, url = {.}, abstract = {Artificial learners often require many more trials than humans or animals when learning motor control tasks in the absence of expert knowledge. We implement two key ingredients of biological learning systems, generalization and incorporation of uncertainty into the decision-making process, to speed up artificial learning. We present a coherent and fully Bayesian framework that allows for efficient artificial learning in the absence of expert knowledge. The success of our learning framework is demonstrated on challenging nonlinear control problems in simulation and in hardware.} } @inproceedings{DeiRas11, cat = {gp rl}, author = {Marc Peter Deisenroth and Carl Edward Rasmussen}, title = {{PILCO}: {A} Model-Based and Data-Efficient Approach to Policy Search}, booktitle = icml28, year = 2011, abstract = {In this paper, we introduce PILCO, a practical, data-efficient model-based policy search method. PILCO reduces model bias, one of the key problems of model-based reinforcement learning, in a principled way. By learning a probabilistic dynamics model and explicitly incorporating model uncertainty into long-term planning, PILCO can cope with very little data and facilitates learning from scratch in only a few trials. Policy evaluation is performed in closed form using state-of-the-art approximate inference. Furthermore, policy gradients are computed analytically for policy improvement. We report unprecedented learning efficiency on challenging and high-dimensional control tasks.}, url = {.}, annote = {web site} } @inproceedings{DeiRasFox11, cat = {rl}, author = {Marc Peter Deisenroth and Carl Edward Rasmussen and Dieter Fox}, title = {Learning to Control a Low-Cost Manipulator using Data-Efficient Reinforcement Learning}, booktitle = rss9, year = 2011, month = {June}, address = {Los Angeles, CA, USA}, abstract = {Over the last years, there has been substantial progress in robust manipulation in unstructured environments. The long-term goal of our work is to get away from precise, but very expensive robotic systems and to develop affordable, potentially imprecise, self-adaptive manipulator systems that can interactively perform tasks such as playing with children. In this paper, we demonstrate how a low-cost off-the-shelf robotic system can learn closed-loop policies for a stacking task in only a handful of trials - from scratch. Our manipulator is inaccurate and provides no pose feedback. For learning a controller in the work space of a Kinect-style depth camera, we use a model-based reinforcement learning technique. Our learning method is data efficient, reduces model bias, and deals with several noise sources in a principled way during long-term planning. We present a way of incorporating state-space constraints into the learning process and analyze the learning gain by exploiting the sequential structure of the stacking task.}, url = {.}, annote = {project site} } @inproceedings{DeiRasPet08, cat = {rl gp}, author = {Marc Peter Deisenroth and Carl Edward Rasmussen and Jan Peters}, title = {Model-Based Reinforcement Learning with Continuous States and Actions}, booktitle = {Proceedings of the 16th European Symposium on Artificial Neural Networks (ESANN 2008)}, year = 2008, pages = {19--24}, address = {Bruges, Belgium}, month = {April}, url = {.}, abstract = {Finding an optimal policy in a reinforcement learning (RL) framework with continuous state and action spaces is challenging. Approximate solutions are often inevitable. GPDP is an approximate dynamic programming algorithm based on Gaussian process (GP) models for the value functions. In this paper, we extend GPDP to the case of unknown transition dynamics. After building a GP model for the transition dynamics, we apply GPDP to this model and determine a continuous-valued policy in the entire state space. We apply the resulting controller to the underpowered pendulum swing up. Moreover, we compare our results on this RL task to a nearly optimal discrete DP solution in a fully known environment.}, annote = {code. slides} } @article{DeiRasPet09, cat = {rl gp}, volume = 72, number = {7--9}, month = {March}, author = {Marc Peter Deisenroth and Carl Edward Rasmussen and Jan Peters}, title = {Gaussian process dynamic programming}, publisher = {Elsevier B. V.}, year = 2009, journal = {Neurocomputing}, pages = {1508--1524}, url = {.}, abstract = {Reinforcement learning (RL) and optimal control of systems with continuous states and actions require approximation techniques in most interesting cases. In this article, we introduce Gaussian process dynamic programming (GPDP), an approximate value function-based RL algorithm. We consider both a classic optimal control problem, where problem-specific prior knowledge is available, and a classic RL problem, where only very general priors can be used. For the classic optimal control problem, GPDP models the unknown value functions with Gaussian processes and generalizes dynamic programming to continuous-valued states and actions. For the RL problem, GPDP starts from a given initial state and explores the state space using Bayesian active learning. To design a fast learner, available data have to be used efficiently. Hence, we propose to learn probabilistic models of the a priori unknown transition dynamics and the value functions on the fly. In both cases, we successfully apply the resulting continuous-valued controllers to the under-actuated pendulum swing up and analyze the performances of the suggested algorithms. It turns out that GPDP uses data very efficiently and can be applied to problems, where classic dynamic programming would be cumbersome.}, annote = {code.}, doi = {10.1016/j.neucom.2008.12.019} } @mastersthesis{Dos09, cat = {np}, author = {Finale Doshi-Velez}, title = {The {I}ndian Buffet Process: {S}calable Inference and Extensions}, school = {University of Cambridge}, year = 2009, address = {Cambridge, UK}, month = {August}, url = {.}, abstract = {Many unsupervised learning problems seek to identify hidden features from observations. In many real-world situations, the number of hidden features is unknown. To avoid specifying the number of hidden features a priori, one can use the Indian Buffet Process (IBP): a nonparametric latent feature model that does not bound the number of active features in a dataset. While elegant, the lack of efficient inference procedures for the IBP has prevented its application in large-scale problems. The core contribution of this thesis are three new inference procedures that allow inference in the IBP to be scaled from a few hundred to 100,000 observations. This thesis contains three parts: (1) An introduction to the IBP and a review of inference techniques and extensions. The first chapters summarise three constructions for the IBP and review all currently published inference techniques. Appendix C reviews extensions of the IBP to date. (2) Novel techniques for scalable Bayesian inference. This thesis presents three new inference procedures: (a) an accelerated Gibbs sampler for efficient Bayesian inference in a broad class of conjugate models, (b) a parallel, asynchronous Gibbs sampler that allows the accelerated Gibbs sampler to be distributed across multiple processors, and (c) a variational inference procedure for the IBP. (3) A framework for structured nonparametric latent feature models. We also present extensions to the IBP to model more sophisticated relationships between the co-occurring hidden features, providing a general framework for correlated non-parametric feature models.} } @inproceedings{Dos09b, author = {Finale Doshi-Velez}, title = {The Infinite Partially Observable {M}arkov Decision Process}, booktitle = nips23, year = 2009, address = {Cambridge, MA, USA}, month = {December}, publisher = mit, url = {.}, abstract = {The Partially Observable Markov Decision Process (POMDP) framework has proven useful in planning domains where agents must balance actions that provide knowledge and actions that provide reward. Unfortunately, most POMDPs are complex structures with a large number of parameters. In many real-world problems, both the structure and the parameters are difficult to specify from domain knowledge alone. Recent work in Bayesian reinforcement learning has made headway in learning POMDP models; however, this work has largely focused on learning the parameters of the POMDP model. We define an infinite POMDP (iPOMDP) model that does not require knowledge of the size of the state space; instead, it assumes that the number of visited states will grow as the agent explores its world and only models visited states explicitly. We demonstrate the iPOMDP on several standard problems.} } @inproceedings{DosGha09, cat = {np mcmc}, booktitle = icml26, title = {Accelerated {Gibbs} sampling for the {Indian} buffet process}, author = {Finale Doshi-Velez and Zoubin Ghahramani}, year = 2009, address = {Montr\'{e}al, QC, Canada}, month = {June}, publisher = {Omnipress}, pages = {273--280}, editor = {L\'{e}on Bottou and Michael Littman}, url = {.}, abstract = {We often seek to identify co-occurring hidden features in a set of observations. The Indian Buffet Process (IBP) provides a non-parametric prior on the features present in each observation, but current inference techniques for the IBP often scale poorly. The collapsed Gibbs sampler for the IBP has a running time cubic in the number of observations, and the uncollapsed Gibbs sampler, while linear, is often slow to mix. We present a new linear-time collapsed Gibbs sampler for conjugate likelihood models and demonstrate its efficacy on large real-world datasets.} } @inproceedings{DosGha09b, cat = {np}, booktitle = {Conference on Uncertainty in Artificial Intelligence (UAI 2009)}, title = {Correlated non-parametric latent feature models}, author = {F. Doshi-Velez and Z. Ghahramani}, year = 2009, address = {Montr\'{e}al, QC, Canada}, month = {June}, pages = {143--150}, publisher = {AUAI Press}, url = {.}, abstract = {We are often interested in explaining data through a set of hidden factors or features. To allow for an unknown number of such hidden features, one can use the IBP: a non-parametric latent feature model that does not bound the number of active features in a dataset. However, the IBP assumes that all latent features are uncorrelated, making it inadequate for many real-world problems. We introduce a framework for correlated non-parametric feature models, generalising the IBP. We use this framework to generate several specific models and demonstrate applications on real-world datasets.} } @inproceedings{DosGha11, cat = {rl}, author = {Finale Doshi-Velez and Zoubin Ghahramani}, year = 2011, title = {A Comparison of Human and Agent Reinforcement Learning in Partially Observable Domains}, booktitle = {33rd Annual Meeting of the Cognitive Science Society}, address = {Boston, MA}, url = {.}, abstract = {It is commonly stated that reinforcement learning (RL) algorithms learn slower than humans. In this work, we investigate this claim using two standard problems from the RL literature. We compare the performance of human subjects to RL techniques. We find that context---the meaningfulness of the observations—--plays a significant role in the rate of human RL. Moreover, without contextual information, humans often fare much worse than classic algorithms. Comparing the detailed responses of humans and RL algorithms, we also find that humans appear to employ rather different strategies from standard algorithms, even in cases where they had indistinguishable performance to them. Our research both sheds light on human RL and provides insights for improving RL algorithms.} } @inproceedings{DosKnoMohGha09, cat = {np approx}, url = {.}, author = {Finale Doshi-Velez and David Knowles and Shakir Mohamed and Zoubin Ghahramani}, title = {Large Scale Non-parametric Inference: {D}ata Parallelisation in the {I}ndian Buffet Process}, booktitle = nips23, pages = {1294--1302}, address = {Cambridge, MA, USA}, publisher = mit, year = 2009, month = {December}, abstract = {Nonparametric Bayesian models provide a framework for flexible probabilistic modelling of complex datasets. Unfortunately, the high-dimensional averages required for Bayesian methods can be slow, especially with the unbounded representations used by nonparametric models. We address the challenge of scaling Bayesian inference to the increasingly large datasets found in real-world applications. We focus on parallelisation of inference in the Indian Buffet Process (IBP), which allows data points to have an unbounded number of sparse latent features. Our novel MCMC sampler divides a large data set between multiple processors and uses message passing to compute the global likelihoods and posteriors. This algorithm, the first parallel inference scheme for IBP-based models, scales to datasets orders of magnitude larger than have previously been possible.} } @inproceedings{DosMilVanTeh09, cat = {np}, author = {Doshi-Velez, F. and Miller, K.T. and {Van Gael}, J. and Teh, Y.W.}, booktitle = aistats12, keywords = {Factor Analysis,IBP,Variational}, mendeley-tags ={Factor Analysis,IBP,Variational}, pages = {137--144}, publisher = jmlr, address = {Clearwater Beach, FL, USA}, title = {Variational inference for the {I}ndian buffet process}, url = {.}, volume = 12, year = 2009, month = {April}, abstract = {The Indian Buffet Process (IBP) is a nonparametric prior for latent feature models in which observations are influenced by a combination of hidden features. For example, images may be composed of several objects and sounds may consist of several notes. Latent feature models seek to infer these unobserved features from a set of observations; the IBP provides a principled prior in situations where the number of hidden features is unknown. Current inference methods for the IBP have all relied on sampling. While these methods are guaranteed to be accurate in the limit, samplers for the IBP tend to mix slowly in practice. We develop a deterministic variational method for inference in the IBP based on a truncated stick-breaking approximation, provide theoretical bounds on the truncation error, and evaluate our method in several data regimes.} } @techreport{DosMilVanTeh09b, cat = {np}, author = {Finale Doshi-Velez and Kurt T. Miller and Jurgen {Van Gael} and Yee Whye Teh}, title = {Variational Inference for the {I}ndian Buffet Process}, institution = {University of Cambridge}, year = 2009, number = {CBL-2009-001}, address = {Computational and Biological Learning Laboratory, Department of Engineering}, month = {April}, url = {.}, abstract = {The Indian Buffet Process (IBP) is a nonparametric prior for latent feature models in which observations are influenced by a combination of hidden features. For example, images may be composed of several objects and sounds may consist of several notes. Latent feature models seek to infer these unobserved features from a set of observations; the IBP provides a principled prior in situations where the number of hidden features is unknown. Current inference methods for the IBP have all relied on sampling. While these methods are guaranteed to be accurate in the limit, samplers for the IBP tend to mix slowly in practice. We develop a deterministic variational method for inference in the IBP based on truncating to infinite models, provide theoretical bounds on the truncation error, and evaluate our method in several data regimes. This technical report is a longer version of Doshi-Velez et al. (2009).} } @article{DosRoy08, author = {Finale Doshi and Nicholas Roy}, title = {Spoken Language Interaction with Model Uncertainty: {A}n Adaptive Human-Robot Interaction System}, journal = {Connection Science}, year = 2008, volume = 20, pages = {290--318}, number = 4, month = {December}, url = {.}, abstract = {Spoken language is one of the most intuitive forms of interaction between humans and agents. Unfortunately, agents that interact with people using natural language often experience communication errors and do not correctly understand the user's intentions. Recent systems have successfully used probabilistic models of speech, language, and user behavior to generate robust dialog performance in the presence of noisy speech recognition and ambiguous language choices, but decisions made using these probabilistic models are still prone to errors due to the complexity of acquiring and maintaining a complete model of human language and behavior. In this paper, we describe a decision-theoretic model for human-robot interaction using natural language. Our algorithm is based on the Partially Observable Markov Decision Process (POMDP), which allows agents to choose actions that are robust not only to uncertainty from noisy or ambiguous speech recognition but also unknown user models. Like most dialog systems, a POMDP is defined by a large number of parameters that may be difficult to specify a priori from domain knowledge, and learning these parameters from the user may require an unacceptably long training period. We describe an extension to the POMDP model that allows the agent to acquire a linguistic model of the user online, including new vocabulary and word choice preferences. Our approach not only avoids a training period of constant questioning as the agent learns, but also allows the agent to actively query for additional information when its uncertainty suggests a high risk of mistakes. We demonstrate our approach both in simulation and on a natural language interaction system for a robotic wheelchair application.} } @inproceedings{DubHwaRanetal04, cat = {np bioinf clust}, author = {A.~Dubey and S.~Hwang and C.~Rangel and Carl Edward Rasmussen and Zoubin Ghahramani and David L.~Wild}, title = {Clustering Protein Sequence and Structure Space with Infinite {G}aussian Mixture Models}, year = 2004, publisher = {World Scientific Publishing}, pages = {399--410}, journal = {Pacific Symposium on Biocomputing 2004; Vol. 9}, address = {Singapore}, abstract = {We describe a novel approach to the problem of automatically clustering protein sequences and discovering protein families, subfamilies etc., based on the thoery of infinite Gaussian mixture models. This method allows the data itself to dictate how many mixture components are required to model it, and provides a measure of the probability that two proteins belong to the same cluster. We illustrate our methods with application to three data sets: globin sequences, globin sequences with known tree-dimensional structures and G-pretein coupled receptor sequences. The consistency of the clusters indicate that that our methods is producing biologically meaningful results, which provide a very good indication of the underlying families and subfamilies. With the inclusion of secondary structure and residue solvent accessibility information, we obtain a classification of sequences of known structure which reflects and extends their SCOP classifications.}, url = {.}, booktitle = {Pacific Symposium on Biocomputing 2004}, location = {The Big Island of Hawaii} } @inproceedings{DuvNicRas11, cat = {gp}, booktitle = nips25, title = {Additive {G}aussian Processes}, author = {David Duvenaud and Hannes Nickisch and Carl Edward Rasmussen}, year = 2011, address = {Granada, Spain}, month = {December}, pages = {1--8}, url = {http://mlg.eng.cam.ac.uk/duvenaud/papers/additive_preprint.pdf}, abstract = {We introduce a Gaussian process model of functions which are $\textitadditive$. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.} } @inproceedings{EatGha09, cat = {gm}, author = {Frederik Eaton and Zoubin Ghahramani}, title = {Choosing a Variable to Clamp: {A}pproximate Inference Using Conditioned Belief Propagation}, booktitle = aistats12, pages = {145--152}, year = 2009, editor = {D. van Dyk and M. Welling}, volume = 5, address = {Clearwater Beach, FL, USA}, month = {April}, publisher = jmlr, url = {.}, annote = {Code (in C++ based on libDAI).}, abstract = {In this paper we propose an algorithm for approximate inference on graphical models based on belief propagation (BP). Our algorithm is an approximate version of Cutset Conditioning, in which a subset of variables is instantiated to make the rest of the graph singly connected. We relax the constraint of single-connectedness, and select variables one at a time for conditioning, running belief propagation after each selection. We consider the problem of determining the best variable to clamp at each level of recursion, and propose a fast heuristic which applies back-propagation to the BP updates. We demonstrate that the heuristic performs better than selecting variables at random, and give experimental results which show that it performs competitively with existing approximate inference algorithms.} } @inproceedings{EicTolZieetal04, author = {Jan Eichhorn and Andreas S.~Tolias and Alexander Zien and Malte Ku{\ss} and Carl Edward Rasmussen and Jason Weston and Nikos K.~Logothetis and Bernhard Sch{\"o}lkopf}, title = {Prediction on Spike Data Using Kernel Algorithms}, year = 2004, volume = 16, publisher = mit, pages = {1367--1374}, editor = {Sebastian Thrun and Lawrence K.~Saul and Bernhard Sch{\"o}lkopf}, address = {Cambridge, MA, USA}, abstract = {We report and compare the performance of different learning algorithms based on data from cortical recordings. The task is to predict the orientation of visual stimuli from the activity of a population of simultaneously recorded neurons. We compare several ways of improving the coding of the input (i.e., the spike data) as well as of the output (i.e., the orientation), and report the results obtained using different kernel algorithms.}, booktitle = nips16, location = {Vancouver, BC, Canada}, URL = {.} } @inproceedings{FraKwoRasSch04, cat = {ssl}, author = {Matthias O.~Franz and Younghee Kwon and Carl Edward Rasmussen and Bernhard Sch{\"o}lkopf}, title = {Semi-supervised kernel regression using whitened function classes}, year = 2004, volume = 3175, booktitle = lncs, publisher = {Springer}, pages = {18--26}, journal = {Pattern Recognition, Proceedings of the 26th {DAGM} Symposium}, editor = {C.~E.~Rasmussen and H.~H.~B{\"u}lthoff and M.~A.~Giese and B.~Sch{\"o}lkopf}, address = {Berlin, Germany}, abstract = {The use of non-orthonormal basis functions in ridge regression leads to an often undesired non-isotropic prior in function space. In this study, we investigate an alternative regularization technique that results in an implicit whitening of the basis functions by penalizing directions in function space with a large prior variance. The regularization term is computed from unlabelled input data that characterizes the input distribution. Tests on two datasets using polynomial basis functions showed an improved average performance compared to standard ridge regression.}, url = {.} } @inproceedings{GhaGriSol07, cat = {np}, month = {July}, author = {Z. Ghahramani and T.L. Griffiths and P. Sollich}, annote = {Includes discussion by David Dunson, and rejoinder.}, booktitle = {Bayesian Statistics 8}, editor = {J.M. Bernardo and M.J. Bayarri and J.O. Berger and A.P. Dawid and D. Heckerman and A.F.M. Smith and M. West}, address = {Oxford, UK}, title = {Bayesian nonparametric latent feature models (with discussion)}, publisher = oup, pages = {201--226}, year = 2007, url = {.}, abstract = {We describe a flexible nonparametric approach to latent variable modelling in which the number of latent variables is unbounded. This approach is based on a probability distribution over equivalence classes of binary matrices with a finite number of rows, corresponding to the data points, and an unbounded number of columns, corresponding to the latent variables. Each data point can be associated with a subset of the possible latent variables, which we refer to as the latent features of that data point. The binary variables in the matrix indicate which latent feature is possessed by which data point, and there is a potentially infinite array of features. We derive the distribution over unbounded binary matrices by taking the limit of a distribution over N×K binary matrices as K→∞. We define a simple generative processes for this distribution which we call the Indian buffet process (IBP; Griffiths and Ghahramani, 2005, 2006) by analogy to the Chinese restaurant process (Aldous, 1985; Pitman, 2002). The IBP has a single hyperparameter which controls both the number of feature per ob ject and the total number of features. We describe a two-parameter generalization of the IBP which has additional flexibility, independently controlling the number of features per object and the total number of features in the matrix. The use of this distribution as a prior in an infinite latent feature model is illustrated, and Markov chain Monte Carlo algorithms for inference are described.} } @inproceedings{GhaHel06, cat = {ir clust}, author = {Zoubin Ghahramani and Katherine A. Heller}, title = {{B}ayesian Sets}, booktitle = nips18, year = 2006, month = {December}, address = {Cambridge, MA, USA}, publisher = mit, editor = {Y. Weiss and B. Sch\"{o}lkopf and J. Platt}, pages = {435--442}, url = {.}, abstract = {Inspired by "Google™ Sets", we consider the problem of retrieving items from a concept or cluster, given a query consisting of a few items from that cluster. We formulate this as a Bayesian inference problem and describe a very simple algorithm for solving it. Our algorithm uses a model-based concept of a cluster and ranks items using a score which evaluates the marginal probability that each item belongs to a cluster containing the query items. For exponential family models with conjugate priors this marginal probability is a simple function of sufficient statistics. We focus on sparse binary data and show that our score can be evaluated exactly using a single sparse matrix multiplication, making it possible to apply our algorithm to very large datasets. We evaluate our algorithm on three datasets: retrieving movies from EachMovie, finding completions of author sets from the NIPS dataset, and finding completions of sets of words appearing in the Grolier encyclopedia. We compare to Google™ Sets and show that Bayesian Sets gives very reasonable set completions.} } @article{GibSaa08, author = {Richard J. Gibbens and Yunus Saat\c{c}i}, title = {Data, modelling and inference in road traffic networks}, journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year = 2008, volume = 366, pages = {1907--1919}, number = 1872, month = {June}, abstract = {In this paper, we study UK road traffic data and explore a range of modelling and inference questions that arise from them. For example, loop detectors on the M25 motorway record speed and flow measurements at regularly spaced locations as well as the entry and exit lanes of junctions. An exploratory study of these data helps us to better understand and quantify the nature of congestion on the road network. From a traveller's perspective it is crucially important to understand the overall journey times and we look at methods to improve our ability to predict journey times given access jointly to both real-time and historical loop detector data. Throughout this paper we will comment on related work derived from US freeway data.}, doi = {10.1098/rsta.2008.0020}, eprint = {http://rsta.royalsocietypublishing.org/content/366/1872/1907.full.pdf+html}, url = {http://rsta.royalsocietypublishing.org/content/366/1872/1907.abstract} } @inproceedings{GirRasQuiMur03, cat = {gp time}, author = {Agathe Girard and Carl Edward Rasmussen and Joaquin Qui{\~n}onero-Candela and Roderick Murray-Smith}, title = {Gaussian Process priors with uncertain inputs --- application to multiple-step ahead time series forecasting}, booktitle = nips15, pages = {529--536}, year = 2003, month = {December}, address = {Cambridge, MA, USA}, editor = {S.~Becker and S.~Thrun and K.~Obermayer}, publisher = mit, url = {.}, abstract = {We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form yt = f(yt-1,...,yt-L), the prediction of y at time t + k is based on the point estimates of the previous outputs. In this paper, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction.} } @article{GlaParKnoetal10, cat = {bioinf}, author = {Daniel Glass and Leopold Parts and David A. Knowles and Abraham Aviv and and Tim D. Spector}, year = 2010, title = {No Correlation Between Childhood Maltreatment and Telomere Length.}, journal = {Biological Psychiatry}, volume = 68, number = 6, pages = {21--22}, abstract = {Telomeres are lengths of repetitive DNA that cap the ends of chromosomes. They protect the ends of the chromosome and shorten with each cell division. Short leukocyte telomere length has been related to a number of age-related diseases. In addition, shorter telomere length has been associated with environmental factors such as smoking and lack of exercise. In a recent issue of Biological Psychiatry, Tyrka et al. (4) published a report suggesting a link between maltreatment in childhood and telomere shortening in 31 subjects. Individuals who had suffered maltreatment had telomere length .70 +/- .24 compared with 1.02 +/- .52 in individuals who had not been abused.}, } @inproceedings{GoeJaeRas06, cat = {np}, author = {Dilan G{\"o}r{\"u}r and Frank J{\"a}kel and Carl Edward Rasmussen}, title = {A Choice Model with Infinitely Many Latent Features}, year = 2006, publisher = {ACM Press}, pages = {361--368}, month = {June}, booktitle = icml23, editor = {W.~W.~Cohen and Andrew Moore}, address = {New York, NY, USA}, doi = {10.1145/1143844.1143890}, abstract = {Elimination by aspects (EBA) is a probabilistic choice model describing how humans decide between several options. The options from which the choice is made are characterized by binary features and associated weights. For instance, when choosing which mobile phone to buy the features to consider may be: long lasting battery, color screen, etc. Existing methods for inferring the parameters of the model assume pre-specified features. However, the features that lead to the observed choices are not always known. Here, we present a non-parametric Bayesian model to infer the features of the options and the corresponding weights from choice data. We use the Indian buffet process (IBP) as a prior over the features. Inference using Markov chain Monte Carlo (MCMC) in conjugate IBP models has been previously described. The main contribution of this paper is an MCMC algorithm for the EBA model that can also be used in inference for other non-conjugate IBP models---this may broaden the use of IBP priors considerably.}, location = {Pittsburgh, PA, USA}, url = {.} } @article{GoeRas10, cat = {np}, title = {{D}irichlet Process {G}aussian Mixture Models: Choice of the base distribution}, author = {Dilan G{\"o}r{\"u}r and Carl Edward Rasmussen}, journal = jcst, publisher = {Science Press}, address = {Beijing, China}, volume = 25, pages = {615--625}, month = {July}, year = 2010, number = 4, url = {.}, doi = {10.1007/s11390-010-9355-8}, abstract = {In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the "correct" number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture (DPM) models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model (DPGMM). We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.} } @inproceedings{GoeRasToletal04, author = {Dilan G{\"o}r{\"u}r and Carl Edward Rasmussen and Andreas S.~Tolias and Fabian Sinz and Nikos K.~Logothetis}, title = {Modelling Spikes with Mixtures of Factor Analysers}, year = 2004, series = lncs, publisher = {Springer}, pages = {391--398}, month = 09, volume = 3175, journal = {Pattern Recognition: Proceedings of the 26th DAGM Symposium}, editor = {C.~E.~Rasmussen and H.~H.~B{\"u}lthoff and B.~Sch{\"o}lkopf and M.~A.~Giese}, address = {Berlin, Germany}, abstract = {Identifying the action potentials of individual neurons from extracellular recordings, known as spike sorting, is a challenging problem. We consider the spike sorting problem using a generative model,mixtures of factor analysers, which concurrently performs clustering and feature extraction. The most important advantage of this method is that it quantifies the certainty with which the spikes are classified. This can be used as a means for evaluating the quality of clustering and therefore spike isolation. Using this method, nearly simultaneously occurring spikes can also be modelled which is a hard task for many of the spike sorting methods. Furthermore, modelling the data with a generative model allows us to generate simulated data.}, booktitle = {DAGM 2004}, location = {T{\"u}bingen, Germany}, url = {.} } @inproceedings{GolAndVanSetetal06, author = {Goldberg, A. B. and Andrzejewski, D. and {Van Gael}, J. and Settles, B. and Zhu, X. and Craven, M.}, shorttitle = {Ranking Biomedical Passages for Relevance and Dive}, title = {Ranking Biomedical Passages for Relevance and Diversity: {U}niversity of {W}isconsin, {M}adison at {TREC} {G}enomics 2006}, booktitle = {Proceedings of the Fifteenth Text REtrieval Conference (TREC 2006)}, url = {.}, year = 2006, month = {November}, address = {Gaithersburg, MD, USA}, abstract = {We report on the University of Wisconsin, Madison's experience in the TREC Genomics 2006 track, which asks participants to retrieve passages from scientific articles that satisfy biologists' information needs. An emphasis is placed on returning relevant passages that discuss different aspects of the topic. Using an off-the-shelf information retrieval (IR) engine, we focused on query generation and reranking query results to encourage relevance and diversity. For query generation, we automatically identify noun phrases from the topic descriptions, and use online resources to gather synonyms as expansion terms. Our first submission uses the baseline IR engine results. We rerank the passages using a naive clustering-based approach in our second run, and we test GRASSHOPPER, a novel graph-theoretic algorithm based on absorbing random walks, in our third run. While our aspect-level results appear to compare favorably with other participants on average, our query generation techniques failed to produce adequate query results for several topics, causing our passage and document-level evaluation scores to suffer. Furthermore, we surprisingly achieved higher aspect-level scores using the initial ranking than our methods aimed specifically at promoting diversity. While this sounds discouraging, we have several ideas as to why this happened and hope to produce new methods that correct these shortcomings.} } @inproceedings{GolZhuVanAnd07, author = {Goldberg, A.B. and Zhu, X. and {Van Gael}, J. and Andrzejewski, D.}, booktitle = {Proceedings of NAACL HLT}, pages = {97--104}, address = {Rochester, NY, USA}, title = {Improving diversity in ranking using absorbing random walks}, url = {.}, year = 2007, month = {April} } @inproceedings{GriGha06, cat = {np}, booktitle = nips18, year = 2006, month = {December}, title = {Infinite Latent Feature Models and the {I}ndian {B}uffet {P}rocess}, author = {T. L. Griffiths and Z. Ghahramani}, address = {Cambridge, MA, USA}, publisher = mit, editor = {Y. Weiss and B. Sch\"{o}lkopf and J. Platt}, pages = {475--482}, url = {.}, abstract = {We define a probability distribution over equivalence classes of binary matrices with a finite number of rows and an unbounded number of columns. This distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features. We identify a simple generative process that results in the same distribution over equivalence classes, which we call the Indian buffet process. We illustrate the use of this distribution as a prior in an infinite latent feature model, deriving a Markov chain Monte Carlo algorithm for inference in this model and applying the algorithm to an image dataset.} } @article{GriGha11, cat = {np review}, volume = 12, month = {April}, author = {Thomas L. Griffiths and Zoubin Ghahramani}, title = {The {Indian} buffet process: {An} introduction and review}, journal = jmlr, pages = {1185--1224}, year = 2011, url = {.}, abstract = {The Indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns. This distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features, or that involve bipartite graphs in which the size of at least one class of nodes is unknown. We give a detailed derivation of this distribution, and illustrate its use as a prior in an infinite latent feature model. We then review recent applications of the Indian buffet process in machine learning, discuss its extensions, and summarize its connections to other stochastic processes.} } @inproceedings{GuaDyNiuetal10, cat = {np clust}, author = {Y. Guan and J. G. Dy and D. Niu and Z. Ghahramani}, title = {Variational inference for nonparametric multiple clustering}, booktitle = {KDD10 Workshop on Discovering, Summarizing, and Using Multiple Clusterings}, address = {Washington, DC, USA}, year = 2010, month = {July}, url = {.}, abstract = {Most clustering algorithms produce a single clustering solution. Similarly, feature selection for clustering tries to find one feature subset where one interesting clustering solution resides. However, a single data set may be multi-faceted and can be grouped and interpreted in many different ways, especially for high dimensional data, where feature selection is typically needed. Moreover, different clustering solutions are interesting for different purposes. Instead of committing to one clustering solution, in this paper we introduce a probabilistic nonparametric Bayesian model that can discover several possible clustering solutions and the feature subset views that generated each cluster partitioning simultaneously. We provide a variational inference approach to learn the features and clustering partitions in each view. Our model allows us not only to learn the multiple clusterings and views but also allows us to automatically learn the number of views and the number of clusters in each view.} } @inproceedings{HalRasMac11, cat = {rl}, author = {Joseph Hall and Carl Edward Rasmussen and Jan Maciejowski}, title = {Reinforcement Learning with Reference Tracking Control in Continuous State Spaces}, url = {.}, booktitle = {Proceedings of 50th IEEE Conference on Decision and Control and European Control Conference}, year = 2011, abstract = {The contribution described in this paper is an algorithm for learning nonlinear, reference tracking, control policies given no prior knowledge of the dynamical system and limited interaction with the system through the learning process. Concepts from the field of reinforcement learning, Bayesian statistics and classical control have been brought together in the formulation of this algorithm which can be viewed as a form indirect self tuning regulator. On the task of reference tracking using the inverted pendulum it was shown to yield generally improved performance on the best controller derived from the standard linear quadratic method using only 30 s of total interaction with the system. Finally, the algorithm was shown to work on the double pendulum proving its ability to solve nontrivial control tasks.} } @article{HanRas94, cat = {approx}, author = {Lars Kai Hansen and Carl Edward Rasmussen}, title = {Pruning from adaptive regularization}, journal = nc, number = 6, volume = 6, pages = {1222--1231}, year = 1994, abstract = {Inspired by the recent upsurge of interest in Bayesian methods we consider adaptive regularization. A generalization based scheme for adaptation of regularization parameters is introduced and compared to Bayesian regularization. We show that pruning arises naturally within both adaptive regularization schemes. As model example we have chosen the simplest possible: estimating the mean of a random variable with known variance. Marked similarities are found between the two methods in that they both involve a "noise limit", below which they regularize with infinite weight decay, i.e., they prune. However, pruning is not always beneficial. We show explicitly that both methods in some cases may increase the generalization error. This corresponds to situations where the underlying assumptions of the regularizer are poorly matched to the environment.}, url = {.}, publisher = mit } @inproceedings{HelWilGha08, author = {Katherine A. Heller and Sinead Williamson and Zoubin Ghahramani}, cat = {clust}, title = {Statistical models for partial membership}, booktitle = icml25, year = 2008, month = {July}, address = {Helsinki, Finland}, publisher = {Omnipress}, editor = {Andrew McCallum and Sam Roweis}, pages = {392--399}, url = {.}, abstract = {We present a principled Bayesian framework for modeling partial memberships of data points to clusters. Unlike a standard mixture model which assumes that each data point belongs to one and only one mixture component, or cluster, a partial membership model allows data points to have fractional membership in multiple clusters. Algorithms which assign data points partial memberships to clusters can be useful for tasks such as clustering genes based on microarray data (Gasch & Eisen, 2002). Our Bayesian Partial Membership Model (BPM) uses exponential family distributions to model each cluster, and a product of these distibtutions, with weighted parameters, to model each datapoint. Here the weights correspond to the degree to which the datapoint belongs to each cluster. All parameters in the BPM are continuous, so we can use Hybrid Monte Carlo to perform inference and learning. We discuss relationships between the BPM and Latent Dirichlet Allocation, Mixed Membership models, Exponential Family PCA, and fuzzy clustering. Lastly, we show some experimental results and discuss nonparametric extensions to our model.} } @inproceedings{HerHerDup11, cat = {np clust}, author = {Daniel Hern\'andez-Lobato and Jos\'e Miguel Hern\'andez-Lobato and Pierre Dupont}, title = {Robust Multi-Class {G}aussian Process Classification}, booktitle = nips25, year = 2011, url = {.}, abstract = {Multi-class Gaussian Processs Classifiers (MGPCs) are often affected by overfitting problems when labeling errors occur far from the decision boundaries. To prevent this, we investigate a robust MGPC (RMGPC) which considers labeling errors independently of their distance to the decision boundaries. Expectation propagation is used for approximate inference. Experiments with several datasets in which noise is injected in the labels illustrate the benefits of RMGPC. This method performs better than other Gaussian process alternatives based on considering latent Gaussian noise or heavy-tailed processes. When no noise is injected in the labels, RMGPC still performs equal or better than the other methods. Finally, we show how RMGPC can be used for successfully indentifying data instances which are difficult to classify correctly in practice.} } @inproceedings{HoeRasHan00, cat = {time}, author = {Pedro A.~d.~F.~R.~H{\o}jen-S{\o}rensen and Carl Edward Rasmussen and Lars Kai Hansen}, title = {{B}ayesian modelling of {fMRI} time series}, booktitle = nips12, year = 2000, pages = {754--760}, url = {.}, editors = {Sara A. Solla, Todd K. Leen and Klaus-Robert M{\"u}ller}, publisher = mit, abstract = {We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte Carlo (MCMC) sampling techniques. The advantage of this method is that detection of short time learning effects between repeated trials is possible since inference is based only on single trial experiments.} } @inproceedings{HueBorKriGha08, cat = {mcmc}, month = {December}, address = {Pisa, Italy}, author = {C. H\"ubler and K. Borgwardt and H.-P. Kriegel and Z. Ghahramani}, note = {ISSN: 1550-4786}, booktitle = {Proceedings of 8th IEEE International Conference on Data Mining (ICDM 2008)}, title = {{M}etropolis algorithms for representative subgraph sampling}, publisher = {IEEE}, pages = {283--292}, year = 2008, url = {.}, abstract = {While data mining in chemoinformatics studied graph data with dozens of nodes, systems biology and the Internet are now generating graph data with thousands and millions of nodes. Hence data mining faces the algorithmic challenge of coping with this significant increase in graph size: Classic algorithms for data analysis are often too expensive and too slow on large graphs.
While one strategy to overcome this problem is to design novel efficient algorithms, the other is to 'reduce' the size of the large graph by sampling. This is the scope of this paper: We will present novel Metropolis algorithms for sampling a 'representative' small subgraph from the original large graph, with 'representative' describing the requirement that the sample shall preserve crucial graph properties of the original graph. In our experiments, we improve over the pioneering work of Leskovec and Faloutsos (KDD 2006), by producing representative subgraph samples that are both smaller and of higher quality than those produced by other methods from the literature.} } @techreport{HusHou11, title = {Adaptive {Bayesian} Qauntum Tomography}, author = {Ferenc Husz\'{a}r and Neil Houlsby}, year = 2011, institution = {University of Cambridge}, annote = {arXiv:1107.0895}, url = {.}, abstract = {In this letter we revisit the problem of optimal design of quantum tomographic experiments. In contrast to previous approaches where an optimal set of measurements is decided in advance of the experiment, we allow for measurements to be adaptively and efficiently re-optimised depending on data collected so far. We develop an adaptive statistical framework based on Bayesian inference and Shannon's information, and demonstrate a ten-fold reduction in the total number of measurements required as compared to non-adaptive methods, including mutually unbiased bases.} } @techreport{HusLac11, title = {A Kernel Approach to Tractable {Bayesian} Nonparametrics}, author = {Ferenc Husz\'{a}r and Simon Lacoste-Julien}, year = 2011, institution = {University of Cambridge}, annote = {arXiv:1103.1761}, url = {.}, abstract = { Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regression can be derived this way from Bayesian linear regression. Despite the success of the Gaussian process framework, the kernel trick is rarely explicitly considered in the Bayesian literature. In this paper, we aim to fill this gap and demonstrate the potential of applying the kernel trick to tractable Bayesian parametric models in a wider context than just regression. As an example, we present an intuitive Bayesian kernel machine for density estimation that is obtained by applying the kernel trick to a Gaussian generative model in feature space.} } @inproceedings{HusNopLen10, author = {Ferenc Husz\'{a}r and Uta Noppeney and M\'{a}t\'{e} Lengyel}, title = {Mind reading by machine learning: {A} doubly {Bayesian} method for inferring mental representations}, booktitle = cogsci32, year = 2010, month = {August}, editor = {S. Ohlsson and R. Catrambone}, publisher = {The Cognitive Science Society}, address = {Austin, TX, USA}, abstract = {A central challenge in cognitive science is to measure and quantify the mental representations humans develop --- in other words, to 'read' subject's minds. In order to eliminate potential biases in reporting mental contents due to verbal elaboration, subjects' responses in experiments are often limited to binary decisions or discrete choices that do not require conscious reflection upon their mental contents. However, it is unclear what such impoverished data can tell us about the potential richness and dynamics of subjects' mental representations. To address this problem, we used ideal observer models that formalise choice behaviour as (quasi-)Bayes-optimal, given subjects' representations in long-term memory, acquired through prior learning, and the stimuli currently available to them. Bayesian inversion of such ideal observer models allowed us to infer subjects' mental representation from their choice behaviour in a variety of psychophysical tasks. The inferred mental representations also allowed us to predict future choices of subjects with reasonable accuracy, even in tasks that were different from those in which the representations were estimated. These results demonstrate a significant potential in standard binary decision tasks to recover detailed information about subjects' mental representations}, url = {.}, annote = {Supplementary material available here.} } @inproceedings{KasVanGraHer10, author = {Kasneci, G. and {Van Gael}, J. and Graepel, T. and Herbrich, R.}, booktitle = {European Conference on Machine Learning (ECML)}, title = {Bayesian Knowledge Corroboration with Logical Rules and User Feedback}, year = 2010, month = {September}, address = {Barcelona, Spain}, url = {.}, abstract = {Current knowledge bases suffer from either low coverage or low accuracy. The underlying hypothesis of this work is that user feedback can greatly improve the quality of automatically extracted knowledge bases. The feedback could help quantify the uncertainty associated with the stored statements and would enable mechanisms for searching, ranking and reasoning at entity-relationship level. Most importantly, a principled model for exploiting user feedback to learn the truth values of statements in the knowledge base would be a major step forward in addressing the issue of knowledge base curation. We present a family of probabilistic graphical models that builds on user feedback and logical inference rules derived from the popular Semantic-Web formalism of RDFS [1]. Through internal inference and belief propagation, these models can learn both, the truth values of the statements in the knowledge base and the reliabilities of the users who give feedback. We demonstrate the viability of our approach in extensive experiments on real-world datasets, with feedback collected from Amazon Mechanical Turk.} } @inproceedings{KimGha08, cat = {gp}, volume = 5342, month = {December}, author = {H.~Kim and Zoubin Ghahramani}, series = lncs, booktitle = {Structural, Syntactic and Statistical Pattern Recognition}, editor = {L. Niels da Vitoria}, title = {Outlier robust {Gaussian} process classification}, address = {Berlin, Germany}, publisher = {Springer Berlin / Heidelberg}, year = 2008, journal = lncs, pages = {896--905}, url = {.}, abstract = {Gaussian process classifiers (GPCs) are a fully statistical model for kernel classification. We present a form of GPC which is robust to labeling errors in the data set. This model allows label noise not only near the class boundaries, but also far from the class boundaries which can result from mistakes in labelling or gross errors in measuring the input features. We derive an outlier robust algorithm for training this model which alternates iterations based on the EP approximation and hyperparameter updates until convergence. We show the usefulness of the proposed algorithm with model selection method through simulation results.} } @inproceedings{KnoGaeGha11, cat = {np approx}, author = {David A.~Knowles and Jurgen Van Gael and Zoubin Ghahramani}, title = {Message Passing Algorithms for the {D}irichlet Diffusion Tree}, booktitle = icml28, year = 2011, abstract = {We demonstrate efficient approximate inference for the Dirichlet Diffusion Tree (Neal, 2003), a Bayesian nonparametric prior over tree structures. Although DDTs provide a powerful and elegant approach for modeling hierarchies they haven't seen much use to date. One problem is the computational cost of MCMC inference. We provide the first deterministic approximate inference methods for DDT models and show excellent performance compared to the MCMC alternative. We present message passing algorithms to approximate the Bayesian model evidence for a specific tree. This is used to drive sequential tree building and greedy search to find optimal tree structures, corresponding to hierarchical clusterings of the data. We demonstrate appropriate observation models for continuous and binary data. The empirical performance of our method is very close to the computationally expensive MCMC alternative on a density estimation problem, and significantly outperforms kernel density estimators.}, url = {.}, annote = {web site} } @inproceedings{KnoGha07, cat = {np bioinf}, url = {.}, author = {David Knowles and Zoubin Ghahramani}, title = {Infinite Sparse Factor Analysis and Infinite Independent Components Analysis}, booktitle = {7th International Conference on Independent Component Analysis and Signal Separation}, year = 2007, month = {September}, address = {London, UK}, publisher = {Springer}, pages = {381--388}, doi = {10.1007/978-3-540-74494-8_48}, abstract = {A nonparametric Bayesian extension of Independent Components Analysis (ICA) is proposed where observed data Y is modelled as a linear superposition, G, of a potentially infinite number of hidden sources, X. Whether a given source is active for a specific data point is specified by an infinite binary matrix, Z. The resulting sparse representation allows increased data reduction compared to standard ICA. We define a prior on Z using the Indian Buffet Process (IBP). We describe four variants of the model, with Gaussian or Laplacian priors on X and the one or two-parameter IBPs. We demonstrate Bayesian inference under these models using a Markov chain Monte Carlo (MCMC) algorithm on synthetic and gene expression data and compare to standard ICA algorithms.} } @inproceedings{KnoGha11a, cat = {np clust}, author = {David A.~Knowles and Zoubin Ghahramani}, title = {Pitman-{Y}or Diffusion Trees}, booktitle = uai27, year = 2011, abstract = {We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.}, url = {.}, annote = {web site} } @article{KnoGha11b, cat = {np bioinf}, author = {David A. Knowles and Zoubin Ghahramani}, year = 2011, title = {Nonparametric {B}ayesian Sparse Factor Models with application to Gene Expression modelling.}, journal = {Annals of Applied Statistics}, volume = 5, number = {2B}, pages = {1534--1552}, url = {.}, abstract = {A nonparametric Bayesian extension of Factor Analysis (FA) is proposed where observed data Y is modeled as a linear superposition, G, of a potentially infinite number of hidden factors, X. The Indian Buffet Process (IBP) is used as a prior on G to incorporate sparsity and to allow the number of latent features to be inferred. The model's utility for modeling gene expression data is investigated using randomly generated data sets based on a known sparse connectivity matrix for E. Coli, and on three biological data sets of increasing complexity.} } @inproceedings{KnoHol09, cat = {bioinf}, author = {David A. Knowles and Susan Holmes}, title = {Statistical tools for ultra-deep pyrosequencing of fast evolving viruses}, booktitle = {NIPS Workshop: Computational Biology}, year = 2009, abstract = {We aim to detect minor variant Hepatitis B viruses (HBV) in 38 pyrosequencing samples from infected individuals. Errors involved in the amplification and ultra deep pyrosequencing (UDPS) of these samples are characterised using HBV plasmid controls. Homopolymeric regions and quality scores are found to be significant covariates in determining insertion and deletion (indel) error rates, but not mismatch rates which depend on the nucleotide transition matrix. This knowledge is used to derive two methods for classifying genuine mutations: a hypothesis testing framework and a mixture model. Using an approximate "ground truth" from a limiting dilution Sanger sequencing run, these methods are shown to outperform the naive percentage threshold approach. The possibility of early stage PCR errors becoming significant is investigated by simulation, which underlines the importance of the initial copy number.}, url = {.}, annote = {web site} } @inproceedings{KnoMin11, cat = {np clust}, author = {David A.~Knowles and Thomas P.~Minka}, title = {Non-conjugate Variational Message Passing for Multinomial and Binary Regression}, booktitle = nips25, year = 2011, abstract = {Variational Message Passing (VMP) is an algorithmic implementation of the Variational Bayes (VB) method which applies only in the special case of conjugate exponential family models. We propose an extension to VMP, which we refer to as Non-conjugate Variational Message Passing (NCVMP) which aims to alleviate this restriction while maintaining modularity, allowing choice in how expectations are calculated, and integrating into an existing message-passing framework: Infer.NET. We demonstrate NCVMP on logistic binary and multinomial regression. In the multinomial case we introduce a novel variational bound for the softmax factor which is tighter than other commonly used bounds whilst maintaining computational tractability.}, url = {.}, annote = {web site supplementary} } @inproceedings{KnoParGlaWin10, cat = {bioinf}, author = {David A. Knowles and Leopold Parts and Daniel Glass and John M. Winn}, title = {Modeling skin and ageing phenotypes using latent variable models in Infer.NET}, booktitle = {NIPS Workshop: Predictive Models in Personalized Medicine Workshop}, year = 2010, abstract = {We demonstrate and compare three unsupervised Bayesian latent variable models implemented in Infer.NET for biomedical data modeling of 42 skin and ageing phenotypes measured on the 12,000 female twins in the Twins UK study. We address various data modeling problems include high missingness, heterogeneous data, and repeat observations. We compare the proposed models in terms of their performance at predicting disease labels and symptoms from available explanatory variables, concluding that factor analysis type models have the strongest statistical performance in this setting. We show that such models can be combined with regression components for improved interpretability.}, url = {.}, annote = {web site} } @inproceedings{KnoParGlaWin11, cat = {bioinf}, author = {David A. Knowles and Leopold Parts and Daniel Glass and John M. Winn}, title = {Inferring a measure of physiological age from multiple ageing related phenotypes}, booktitle = {NIPS Workshop: From Statistical Genetics to Predictive Models in Personalized Medicine}, year = 2011, abstract = {What is ageing? One definition is simultaneous degradation of multiple organ systems. Can an individual be said to be "old" or "young" for their (chronological) age in a scientifically meaningful way? We investigate these questions using ageing related phenotypes measured on the 12,000 female twins in the Twins UK study. We propose a simple linear model of ageing, which allows a latent adjustment to be made to an individual's chronological age to give her "physiological age", shared across the observed phenotypes. We note problems with the analysis resulting from the linearity assumption and show how to alleviate these issues using a non-linear extension. We find more gene expression probes are significantly associated with our measurement of physiological age than to chronological age. }, url = {.}, annote = {web site} } @inproceedings{KocBanLiketal03, cat = {gp}, booktitle = {IFAC Internaltional Conference on Intelligent Control Systems and Signal Processing}, title = {A case based comparison of identification with neural network and {G}aussian process models}, author = {Ju{\v s} Kocijan and Bla{\v z} Banko and Bojan Likar and Agathe Girard and Roderick Murray-Smith and Carl Edward Rasmussen}, year = 2003, volume = 1, pages = {137--142}, url = {.}, abstract = {In this paper an alternative approach to black-box identification of non-linear dynamic systems is compared with the more established approach of using artificial neural networks. The Gaussian process prior approach is a representative of non-parametric modelling approaches. It was compared on a pH process modelling case study. The purpose of modelling was to use the model for control design. The comparison revealed that even though Gaussian process models can be effectively used for modelling dynamic systems caution has to be axercised when signals are selected.} } @inproceedings{KocMurRasGir04, cat = {gp rl}, author = {Ju{\v s} Kocijan and Roderick Murray-Smith and Carl Edward Rasmussen and Agathe Girard}, title = {Gaussian process model based predictive control}, year = 2004, pages = {2214--2219}, journal = {Proceedings of the ACC 2004}, abstract = {Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identi cation of non-linear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. Gaussian process models contain noticeably less coef cients to be optimised. This paper illustrates possible application of Gaussian process models within model-based predictive control. The extra information provided within Gaussian process model is used in predictive control, where optimisation of control signal takes the variance information into account. The predictive control principle is demonstrated on control of pH process benchmark.}, booktitle = {American Control Conference}, location = {Boston, MA}, url = {.} } @inproceedings{KocMurRasLik03, cat = {gp rl}, title = {Predictive control with {G}aussian process models}, author = {Ju{\v s} Kocijan and Roderick Murray-Smith and Carl Edward Rasmussen and Bojan Likar}, editor = {B.~Zajc and M.~Tkal}, pages = {352--356}, url = {.}, year = 2003, booktitle = {IEEE Region 8 Eurocon 2003: Computer as a Tool}, abstract = {This paper describes model-based predictive control based on Gaussian processes. Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. It offers more insight in variance of obtained model response, as well as fewer parameters to determine than other models. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. This property is used in predictive control, where optimisation of control signal takes the variance information into account. The predictive control principle is demonstrated on a simulated example of nonlinear system.} } @techreport{KusPfiCsaRas05, cat = {gp}, author = {Malte Ku{\ss} and Tobias Pfingsten and Lehel Csat{\`o} and Carl Edward Rasmussen}, title = {Approximate Inference for Robust {G}aussian Process Regression}, year = 2005, institution = {Max Planck Institute for Biological Cybernetics}, number = 136, address = {T{\"u}bingen, Germany}, abstract = {Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectation-propagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectation-propagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling.}, url = {.} } @article{KusRas05, cat = {gp approx}, author = {Malte {Ku\ss} and Carl Edward Rasmussen}, title = {Assessing Approximate Inference for Binary {G}aussian Process Classification}, journal = jmlr, year = 2005, volume = 6, pages = {1679--1704}, url = {http://www.jmlr.org/papers/volume6/kuss05a/kuss05a.pdf}, abstract = {Gaussian process priors can be used to define flexible, probabilistic classification models. Unfortunately exact Bayesian inference is analytically intractable and various approximation techniques have been proposed. In this work we review and compare Laplace's method and Expectation Propagation for approximate Bayesian inference in the binary Gaussian process classification model. We present a comprehensive comparison of the approximations, their predictive performance and marginal likelihood estimates to results obtained by MCMC sampling. We explain theoretically and corroborate empirically the advantages of Expectation Propagation compared to Laplace's method.} } @inproceedings{KusRas06, cat = {gp rl}, author = {Malte Ku{\ss} and Carl Edward Rasmussen}, title = {Assessing Approximations for {G}aussian Process Classification}, year = 2006, publisher = mit, pages = {699--706}, month = {April}, booktitle = nips18, editor = {Y.~Weiss and B.~Sch{\"o}lkopf and J.~Platt}, address = {Cambridge, MA, USA}, abstract = {Gaussian processes are attractive models for probabilistic classification but unfortunately exact inference is analytically intractable. We compare Laplace's method and Expectation Propagation (EP) focusing on marginal likelihood estimates and predictive performance. We explain theoretically and corroborate empirically that EP is superior to Laplace. We also compare to a sophisticated MCMC scheme and show that EP is surprisingly accurate.}, location = {Whistler, BC, Canada}, URL = {.} } @inproceedings{LacHusGha11, cat = {approx gp}, url = {.}, author = {Simon Lacoste-Julien and Ferenc Husz\'{a}r and Zoubin Ghahramani}, title = {Approximate Inference for the Loss-Calibrated {B}ayesian}, booktitle = aistats14, year = 2011, editor = {Geoff Gordon and David Dunson}, volume = 15, pages = {416--424}, address = {Fort Lauderdale, FL, USA}, month = {April}, publisher = jmlr, abstract = {We consider the problem of approximate inference in the context of Bayesian decision theory. Traditional approaches focus on approximating general properties of the posterior, ignoring the decision task -- and associated losses -- for which the posterior could be used. We argue that this can be suboptimal and propose instead to \emph{loss-calibrate} the approximate inference methods with respect to the decision task at hand. We present a general framework rooted in Bayesian decision theory to analyze approximate inference from the perspective of losses, opening up several research directions. As a first loss-calibrated approximate inference attempt, we propose an EM-like algorithm on the Bayesian posterior risk and show how it can improve a standard approach to Gaussian process classification when losses are asymmetric.} } @article{LazQuiRasFig10, cat = {gp}, author = {Miguel L\'azaro-Gredilla and Joaquin Qui{\~n}onero-Candela and Carl Edward Rasmussen and An\'{i}bal Figueiras-Vidal}, title = {Sparse Spectrum {G}aussian Process Regression}, journal = jmlr, url = {http://jmlr.csail.mit.edu/papers/volume11/lazaro-gredilla10a/lazaro-gredilla10a.pdf}, volume = 11, pages = {1865--1881}, month = {June}, year = 2010, abstract = {We present a new sparse Gaussian Process (GP) model for regression. The key novel idea is to sparsify the \emph{spectral representation} of the GP. This leads to a simple, practical algorithm for regression tasks. We compare the achievable trade-offs between predictive accuracy and computational requirements, and show that these are typically superior to existing state-of-the-art sparse approximations. We discuss both the weight space and function space representations, and note that the new construction implies priors over functions which are always stationary, and can approximate any covariance function in this class.} } @article{LesChaKleetal10, author = {J. Leskovec and D. Chakrabarti and J. Kleinberg and C. Faloutsos and Z. Ghahramani}, year = 2010, title = {Kronecker Graphs: An Approach to Modeling Networks}, journal = jmlr, volume = {11(Feb)}, pages = {985--1042}, url = {.}, abstract = {How can we generate realistic networks? In addition, how can we do so with a mathematically tractable model that allows for rigorous analysis of network properties? Real networks exhibit a long list of surprising properties: Heavy tails for the in- and out-degree distribution, heavy tails for the eigenvalues and eigenvectors, small diameters, and densification and shrinking diameters over time. Current network models and generators either fail to match several of the above properties, are complicated to analyze mathematically, or both. Here we propose a generative model for networks that is both mathematically tractable and can generate networks that have all the above mentioned structural properties. Our main idea here is to use a non-standard matrix operation, the Kronecker product, to generate graphs which we refer to as "Kronecker graphs".
First, we show that Kronecker graphs naturally obey common network properties. In fact, we rigorously prove that they do so. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks.
We then present KRONFIT, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super-exponential time. In contrast, KRONFIT takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on a wide range of large real and synthetic networks show that KRONFIT finds accurate parameters that very well mimic the properties of target networks. In fact, using just four parameters we can accurately model several aspects of global network structure. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null-models, anonymization, extrapolations, and graph summarization.} } @article{LipGhaBor10, cat = {bioinf}, author = {C. Lippert and Z. Ghahramani and K. Borgwardt}, title = {Gene function prediction from synthetic lethality networks via ranking on demand}, journal = {Bioinformatics}, year = 2010, volume = 26, pages = {912--918}, url = {.}, abstract = {Motivation: Synthetic lethal interactions represent pairs of genes whose individual mutations are not lethal, while the double mutation of both genes does incur lethality. Several studies have shown a correlation between functional similarity of genes and their distances in networks based on synthetic lethal interactions. However, there is a lack of algorithms for predicting gene function from synthetic lethality interaction networks.
Results: In this article, we present a novel technique called kernelROD for gene function prediction from synthetic lethal interaction networks based on kernel machines. We apply our novel algorithm to Gene Ontology functional annotation prediction in yeast. Our experiments show that our method leads to improved gene function prediction compared with state-of-the-art competitors and that combining genetic and congruence networks leads to a further improvement in prediction accuracy.} } @inproceedings{LipSteGhaetal09, cat = {bioinf}, volume = 5, author = {C. Lippert and O. Stegle and Z. Ghahramani and K. Borgwardt}, note = {ISSN: 1938-7228}, booktitle = aistats12, editor = {D. van Dyk and M. Welling}, title = {A kernel method for unsupervised structured network inference}, publisher = jmlr, year = 2009, month = {April}, address = {Clearwater Beach, FL, USA}, pages = {368--375}, url = {.}, abstract = {Network inference is the problem of inferring edges between a set of real-world objects, for instance, interactions between pairs of proteins in bioinformatics. Current kernel-based approaches to this problem share a set of common features: (i) they are supervised and hence require labeled training data; (ii) edges in the network are treated as mutually independent and hence topological properties are largely ignored; (iii) they lack a statistical interpretation. We argue that these common assumptions are often undesirable for network inference, and propose (i) an unsupervised kernel method (ii) that takes the global structure of the network into account and (iii) is statistically motivated. We show that our approach can explain commonly used heuristics in statistical terms. In experiments on social networks, dfferent variants of our method demonstrate appealing predictive performance.} } @inproceedings{MacBusCunetal11, cat = {time}, booktitle = nips25, title = {Empirical models of spiking in neural populations}, author = {J. H. Macke and L. Busing and J. P. Cunningham and B. M. Yu and K. V. Shenoy and M. Sahani}, year = 2011, address = {Granada, Spain}, month = {December}, pages = {1--8}, url = {.}, abstract = {Neurons in the neocortex code and compute as part of a locally interconnected population. Large-scale multi-electrode recording makes it possible to access these population processes empirically by fitting statistical models to unaveraged data. What statistical structure best describes the concurrent spiking of cells within a local network? We argue that in the cortex, where firing exhibits extensive correlations in both time and space and where a typical sample of neurons still reflects only a very small fraction of the local population, the most appropriate model captures shared variability by a low-dimensional latent process evolving with smooth dynamics, rather than by putative direct coupling. We test this claim by comparing a latent dynamical model with realistic spiking observations to coupled generalised linear spike-response models (GLMs) using cortical recordings. We find that the latent dynamical approach outperforms the GLM in terms of goodness-of- fit, and reproduces the temporal correlations in the data more accurately. We also compare models whose observations models are either derived from a Gaussian or point-process models, finding that the non-Gaussian model provides slightly better goodness-of-fit and more realistic population spike counts.} } @inproceedings{MchRas11, cat = {gp}, booktitle = nips25, title = {Gaussian Process Training with Input Noise}, author = {Andrew McHutchon and Carl Edward Rasmussen}, year = 2011, address = {Granada, Spain}, month = {December}, url = {http://mlg.eng.cam.ac.uk/mchutchon/papers/NIGP.pdf}, abstract = {In standard Gaussian Process regression input locations are assumed to be noise free. We present a simple yet effective GP model for training on input points corrupted by i.i.d. Gaussian noise. To make computations tractable we use a local linear expansion about each input point. This allows the input noise to be recast as output noise proportional to the squared gradient of the GP posterior mean. The input noise hyperparameters are trained alongside other hyperparameters by the usual method of maximisation of the marginal likelihood, and allow estimation of the noise levels on each input dimension. Training uses an iterative scheme, which alternates between optimising the hyperparameters and calculating the posterior gradient. Analytic predictive moments can then be found for Gaussian distributed test points. We compare our model to others over a range of different regression problems and show that it improves over current methods.} } @inproceedings{MeeGhaNeaetal07, cat = {np}, month = {September}, author = {E. Meeds and Z. Ghahramani and R. Neal and S.T. Roweis}, series = {Bradford Books}, note = {Online contents gives pages 1002--1009, and 977--984 on pdf contents.}, booktitle = nips19, editor = {B. Sch\"olkopf and J. Platt and T. Hofmann}, title = {Modelling dyadic data with binary latent factors}, address = {Cambridge, MA, USA}, publisher = mit, year = 2007, pages = {977--984}, url = {.}, abstract = {We introduce binary matrix factorization, a novel model for unsupervised matrix decomposition. The decomposition is learned by fitting a non-parametric Bayesian probabilistic model with binary latent variables to a matrix of dyadic data. Unlike bi-clustering models, which assign each row or column to a single cluster based on a categorical hidden feature, our binary feature model reflects the prior belief that items and attributes can be associated with more than one latent cluster at a time. We provide simple learning and inference rules for this new model and show how to extend it to an infinite model in which the number of features is not a priori fixed but is allowed to grow with the size of the data.} } @phdthesis{Moh11, author = {Shakir Mohamed}, title = {Generalised {B}ayesian Matrix Factorisation Models}, school = {University of Cambridge, Department of Engineering}, year = 2011, address = {Cambridge, UK}, abstract = {Factor analysis and related models for probabilistic matrix factorisation are of central importance to the unsupervised analysis of data, with a colourful history more than a century long. Probabilistic models for matrix factorisation allow us to explore the underlying structure in data, and have relevance in a vast number of application areas including collaborative filtering, source separation, missing data imputation, gene expression analysis, information retrieval, computational finance and computer vision, amongst others.
This thesis develops generalisations of matrix factorisation models that advance our understanding and enhance the applicability of this important class of models. The generalisation of models for matrix factorisation focuses on three concerns: widening the applicability of latent variable models to the diverse types of data that are currently available; considering alternative structural forms in the underlying representations that are inferred; and including higher order data structures into the matrix factorisation framework. These three issues reflect the reality of modern data analysis and we develop new models that allow for a principled exploration and use of data in these settings. We place emphasis on Bayesian approaches to learning and the advantages that come with the Bayesian methodology. Our port of departure is a generalisation of latent variable models to members of the exponential family of distributions. This generalisation allows for the analysis of data that may be real-valued, binary, counts, non-negative or a heterogeneous set of these data types. The model unifies various existing models and constructs for unsupervised settings, the complementary framework to the generalised linear models in regression.
Moving to structural considerations, we develop Bayesian methods for learning sparse latent representations. We define ideas of weakly and strongly sparse vectors and investigate the classes of prior distributions that give rise to these forms of sparsity, namely the scale-mixture of Gaussians and the spike-and-slab distribution. Based on these sparsity favouring priors, we develop and compare methods for sparse matrix factorisation and present the first comparison of these sparse learning approaches. As a second structural consideration, we develop models with the ability to generate correlated binary vectors. Moment-matching is used to allow binary data with specified correlation to be generated, based on dichotomisation of the Gaussian distribution. We then develop a novel and simple method for binary PCA based on Gaussian dichotomisation. The third generalisation considers the extension of matrix factorisation models to multi-dimensional arrays of data that are increasingly prevalent. We develop the first Bayesian model for non-negative tensor factorisation and explore the relationship between this model and the previously described models for matrix factorisation.}, url = {.} } @inproceedings{MohHelGha08, title = {Bayesian Exponential Family {PCA}}, author = {Shakir Mohamed and Katherine A. Heller and Zoubin Ghahramani}, booktitle = nips21, editor = {D. Koller and D. Schuurmans and Y. Bengio and L. Bottou}, pages = {1089--1096}, year = 2009, month = {December}, address = {Cambridge, MA, USA}, publisher = mit, url = {.}, abstract = {Principal Components Analysis (PCA) has become established as one of the key tools for dimensionality reduction when dealing with real valued data. Approaches such as exponential family PCA and non-negative matrix factorisation have successfully extended PCA to non-Gaussian data types, but these techniques fail to take advantage of Bayesian inference and can suffer from problems of overfitting and poor generalisation. This paper presents a fully probabilistic approach to PCA, which is generalised to the exponential family, based on Hybrid Monte Carlo sampling. We describe the model which is based on a factorisation of the observed data matrix, and show performance of the model on both synthetic and real data.}, annote = {spotlight.} } @article{MovChoKnoetal11, cat = {bioinf}, author = {Mehregan Movassagh and Mun-Kit Choy and David A. Knowles and Lina Cordeddu and Syed Haider and Thomas Down and Lee Siggens and Ana Vujic and Ilenia Simeoni and Chris Penkett and Martin Goddard and Pietro Lio and Martin Bennett and Roger Foo}, title = {Distinct epigenomic features in human cardiomyopathy}, url = {http://circ.ahajournals.org/content/early/2011/10/24/CIRCULATIONAHA.111.040071.abstract}, journal = {Circulation, American Heart Association}, year = 2011, abstract = {Background. The epigenome refers to marks on the genome including DNA methylation and histone modifications that regulate the expression of underlying genes. A consistent profile of gene expression changes in end- stage cardiomyopathy led us to hypothesise that distinct global patterns of the epigenome may also exist. Methods and Results. We constructed genome-wide maps of DNA methylation and Histone-3 Lysine-36 tri-methylation (H3K36me3)-enrichment for cardiomyopathic and normal human hearts. 506Mb of sequence per library was generated by high-throughput sequencing, covering 24 million out of the 28 million CG di-nucleotides in the human genome. DNA methylation was significantly different in promoter CpG-islands (CGI), intra-genic CGI, gene bodies and H3K36me3-enriched regions of the genome. Moreover DNA methylation differences were present in promoters of upregulated genes but not down-regulated genes. The profile of H3K36me3-enrichment itself was also significantly different in protein-coding regions of the genome. Conclusions. Distinct epigenomic patterns exist in important DNA elements of the human cardiac genome in end-stage cardiomyopathy. If epigenomic patterns track with disease progression, assays for the epigenome may be more useful than quantification of mRNA for assessing prognosis in heart failure. These results open up an important new horizon of research and further studies will be needed to determine how epigenomics contribute to altered gene expression in cardiomyopathy.} } @inproceedings{MurSbaRasGir03, cat = {gp rl}, author = {Roderick Murray-Smith and Daniel Sbarbaro and Carl Edward Rasmussen and Agathe Girard}, title = {Adaptive, Cautious, Predictive control with {G}aussian Process Priors}, year = 2003, publisher = {Elsevier Science Ltd}, pages = {1195-1200}, month = {August}, journal = {Proceedings of the 13th IFAC Symposium on System Identification}, editor = {P.~Van den Hof and B.~Wahlberg and S.~Weiland}, url = {.}, address = {Oxford, UK}, abstract = {Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made over a k-step horizon. The expected value of a quadratic cost function is minimised, over this prediction horizon, without ignoring the variance of the model predictions. The general method and its main features are illustrated on a simulation example.}, booktitle = {IFAC SYSID 2003}, location = {Rotterdam, The Netherlands} } @article{NicRas08, cat = {gp approx}, author = {Hannes Nickisch and Carl Edward Rasmussen}, title = {Approximations for Binary {G}aussian Process Classification}, year = 2008, volume = 9, pages = {2035--2078}, month = {October}, journal = jmlr, abstract = {We provide a comprehensive overview of many recent algorithms for approximate inference in Gaussian process models for probabilistic binary classification. The relationships between several approaches are elucidated theoretically, and the properties of the different algorithms are corroborated by experimental results. We examine both 1) the quality of the predictive distributions and 2) the suitability of the different marginal likelihood approximations for model selection (selecting hyperparameters) and compare to a gold standard based on MCMC. Interestingly, some methods produce good predictive distributions although their marginal likelihood approximations are poor. Strong conclusions are drawn about the methods: The Expectation Propagation algorithm is almost always the method of choice unless the computational budget is very tight. We also extend existing methods in various ways, and provide unifying code implementing all approaches.}, url = {http://www.jmlr.org/papers/volume9/nickisch08a/nickisch08a.pdf} } @inproceedings{NicRas10, cat = {gp}, author = {Hannes Nickisch and Carl Edward Rasmussen}, title = {Gaussian Mixture Modeling with {G}aussian Process Latent Variable Models}, publisher = {Springer}, series = lncs, year = 2010, month = {September}, address = {Darmstadt, Germany}, url = {.}, booktitle = {Proceedings of the 32nd DAGM Symposium on Pattern Recognition}, abstract = {Density modeling is notoriously difficult for high dimensional data. One approach to the problem is to search for a lower dimensional manifold which captures the main characteristics of the data. Recently, the Gaussian Process Latent Variable Model (GPLVM) has successfully been used to find low dimensional manifolds in a variety of complex data. The GPLVM consists of a set of points in a low dimensional latent space, and a stochastic map to the observed space. We show how it can be interpreted as a density model in the observed space. However, the GPLVM is not trained as a density model and therefore yields bad density estimates. We propose a new training strategy and obtain improved generalisation performance and better density estimates in comparative evaluations on several benchmark data sets.}, doi = {10.1007/978-3-642-15986-2_28} } @inproceedings{Orb09, cat = {np}, author = {Peter Orbanz}, title = {Construction of Nonparametric {B}ayesian Models from Parametric {B}ayes Equations}, url = {.}, publisher = mit, booktitle = nips22, year = 2009, pages = {1392--1400}, editor = {Y.~Bengio and D.~Schuurmans and J.~Lafferty and C.~K.~I.~Williams and A.~Culotta}, abstract = {We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in nonparametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finitedimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.}, annote = {Supplements (proofs) and techreport version} } @phdthesis{Ort11, cat = {rl}, author = {Pedro A.~Ortega}, title = {A Unified Framework for Resource-Bounded Agents Interacting with an Unknown Environment}, school = {Department of Engineering, University of Cambridge}, year = 2011, abstract = {The aim of this thesis is to present a mathematical framework for conceptualizing and constructing adaptive autonomous systems under resource constraints. The first part of this thesis contains a concise presentation of the foundations of classical agency: namely the formalizations of decision making and learning. Decision making includes: (a) subjective expected utility (SEU) theory, the framework of decision making under uncertainty; (b) the maximum SEU principle to choose the optimal solution; and (c) its application to the design of autonomous systems, culminating in the Bellman optimality equations. Learning includes: (a) Bayesian probability theory, the theory for reasoning under uncertainty that extends logic; and (b) Bayes-Optimal agents, the application of Bayesian probability theory to the design of optimal adaptive agents. Then, two major problems of the maximum SEU principle are highlighted: (a) the prohibitive computational costs and (b) the need for the causal precedence of the choice of the policy. The second part of this thesis tackles the two aforementioned problems. First, an information-theoretic notion of resources in autonomous systems is established. Second, a framework for resource-bounded agency is introduced. This includes: (a) a maximum bounded SEU principle that is derived from a set of axioms of utility; (b) an axiomatic model of probabilistic causality, which is applied for the formalization of autonomous systems having uncertainty over their policy and environment; and (c) the Bayesian control rule, which is derived from the maximum bounded SEU principle and the model of causality, implementing a stochastic adaptive control law that deals with the case where autonomous agents are uncertain about their policy and environment.}, url = {http://www.dcc.uchile.cl/~peortega/home/lib/exe/fetch.php?id=autonomous_agents&cache=cache&media=thesis.pdf} } @inproceedings{OrtBra10a, cat = {rl}, author = {Pedro A.~Ortega and Daniel A.~Braun}, title = {A conversion between utility and information}, booktitle = {The third conference on artificial general intelligence}, publisher = {Atlantis Press}, address = {Paris}, pages = {115--120}, year = 2010, url = {http://agi-conf.org/2010/wp-content/uploads/2009/06/paper_35.pdf}, abstract = {Rewards typically express desirabilities or preferences over a set of alternatives. Here we propose that rewards can be defined for any probability distribution based on three desiderata, namely that rewards should be real- valued, additive and order-preserving, where the later implies that more probable events should also be more desirable. Our main result states that rewards are then uniquely determined by the negative information content. To analyze stochastic processes, we define the utility of a realization as its reward rate. Under this interpretation, we show that the expected utility of a stochastic process is its negative entropy rate. Furthermore, we apply our results to analyze agent-environment interactions. We show that the expected utility that will actually be achieved by the agent is given by the negative cross-entropy from the input-output (I/O) distribution of the coupled interaction system and the agent's I/O distribution. Thus, our results allow for an information-theoretic interpretation of the notion of utility and the characterization of agent-environment interactions in terms of entropy dynamics.} } @inproceedings{OrtBra10b, cat = {rl}, author = {Pedro A.~Ortega and Daniel A.~Braun}, title = {A {B}ayesian rule for adaptive control based on causal interventions}, booktitle = {The third conference on artificial general intelligence}, publisher = {Atlantis Press}, address = {Paris}, pages = {115--120}, year = 2010, url = {http://agi-conf.org/2010/wp-content/uploads/2009/06/paper_28.pdf}, abstract = {Explaining adaptive behavior is a central problem in artificial intelligence research. Here we formalize adaptive agents as mixture distributions over sequences of inputs and outputs (I/O). Each distribution of the mixture constitutes a "possible world", but the agent does not know which of the possible worlds it is actually facing. The problem is to adapt the I/O stream in a way that is compatible with the true world. A natural measure of adaptation can be obtained by the Kullback Leibler (KL) divergence between the I/O distribution of the true world and the I/O distribution expected by the agent that is uncertain about possible worlds. In the case of pure input streams, the Bayesian mixture provides a well-known solution for this problem. We show, however, that in the case of I/O streams this solution breaks down, because outputs are issued by the agent itself and require a different probabilistic syntax as provided by intervention calculus. Based on this calculus, we obtain a Bayesian control rule that allows modeling adaptive behavior with mixture distributions over I/O streams. This rule might allow for a novel approach to adaptive control based on a minimum KL-principle.} } @article{OrtBra10c, cat = {rl}, author = {Pedro A.~Ortega and Daniel A.~Braun}, title = {A minimum relative entropy principle for learning and acting}, journal = {Journal of Artificial Intelligence Research}, volume = 38, pages = {475--511}, year = 2010, url = {http://www.jair.org/vol/vol38.html}, abstract = {This paper proposes a method to construct an adaptive agent that is universal with respect to a given class of experts, where each expert is designed specifically for a particular environment. This adaptive control problem is formalized as the problem of minimizing the relative entropy of the adaptive agent from the expert that is most suitable for the unknown environment. If the agent is a passive observer, then the optimal solution is the well-known Bayesian predictor. However, if the agent is active, then its past actions need to be treated as causal interventions on the I/O stream rather than normal probability conditions. Here it is shown that the solution to this new variational problem is given by a stochastic controller called the Bayesian control rule, which implements adaptive behavior as a mixture of experts. Furthermore, it is shown that under mild assumptions, the Bayesian control rule converges to the control law of the most suitable expert.}, doi = {10.1613/jair.3062} } @techreport{OrtBra10d, cat = {rl}, author = {Pedro A.~Ortega and Daniel A.~Braun}, title = {An axiomatic formalization of bounded rationality based on a utility-information equivalence}, institution = {Dept. of Engineering, University of Cambridge}, year = 2010, url = {http://arxiv.org/abs/1007.0940}, abstract = {Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that considers resource costs. Agents are formalized as probability measures over input-output streams. We postulate that any such probability measure can be assigned a corresponding conjugate utility function based on three axioms: utilities should be real-valued, additive and monotonic mappings of probabilities. We show that these axioms enforce a unique conversion law between utility and probability (and thereby, information). Moreover, we show that this relation can be characterized as a variational principle: given a utility function, its conjugate probability measure maximizes a free utility functional. Transformations of probability measures can then be formalized as a change in free utility due to the addition of new constraints expressed by a target utility function. Accordingly, one obtains a criterion to choose a probability measure that trades off the maximization of a target utility function and the cost of the deviation from a reference distribution. We show that optimal control, adaptive estimation and adaptive control problems can be solved this way in a resource-efficient way. When resource costs are ignored, the MEU principle is recovered. Our formalization might thus provide a principled approach to bounded rationality that establishes a close link to information theory.} } @inproceedings{OrtBra11, cat = {rl}, author = {Pedro A.~Ortega and Daniel A.~Braun}, title = {Information, Utility and Bounded Rationality}, booktitle = {The fourth conference on artificial general intelligence}, year = 2011, volume = 6830, pages = {269--274}, series = {Lecture Notes on Artificial Intelligence}, publisher = {Springer-Verlag}, abstract = {Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we employ an axiomatic framework for bounded rational decision-making based on a thermodynamic interpretation of resource costs as information costs. This leads to a variational free utility principle akin to thermodynamical free energy that trades off utility and information costs. We show that bounded optimal control solutions can be derived from this variational principle, which leads in general to stochastic policies. Furthermore, we show that risk-sensitive and robust (minimax) control schemes fall out naturally from this framework if the environment is considered as a bounded rational and perfectly rational opponent, respectively. When resource costs are ignored, the maximum expected utility principle is recovered.}, url = {http://www.dcc.uchile.cl/~peortega/home/lib/exe/fetch.php?id=autonomous_agents&cache=cache&media=infoutilityboundedrationality.pdf} } @inproceedings{OrtBraGod11, cat = {rl}, author = {Pedro A.~Ortega and Daniel A.~Braun and Simon Godsill}, title = {Reinforcement Learning and the {B}ayesian Control Rule}, booktitle = {The fourth conference on artificial general intelligence}, year = 2011, volume = 6830, pages = {281--285}, series = {Lecture Notes on Artificial Intelligence}, publisher = {Springer-Verlag}, abstract = {We present an actor-critic scheme for reinforcement learning in complex domains. The main contribution is to show that planning and I/O dynamics can be separated such that an intractable planning problem reduces to a simple multi-armed bandit problem, where each lever stands for a potentially arbitrarily complex policy. Furthermore, we use the Bayesian control rule to construct an adaptive bandit player that is universal with respect to a given class of optimal bandit players, thus indirectly constructing an adaptive agent that is universal with respect to a given class of policies.}, url = {http://www.dcc.uchile.cl/~peortega/home/lib/exe/fetch.php?id=autonomous_agents&cache=cache&media=actor-critic.pdf} } @incollection{PerGhaPon07, cat = {gm}, month = {September}, author = {F. P\'{e}rez-Cruz and Zoubin Ghahramani and M. Pontil}, note = {Chapter 12.}, booktitle = {Predicting Structured Data}, editor = {G.~H.~Bakir and T.~Hofmann and B.~Sch\"olkopf and A.~J.~Smola and B.~Taskar and S.~V.~N.~Vishwanathan}, address = {Cambridge, MA, USA}, title = {Conditional graphical models}, publisher = mit, year = 2007, pages = {265--282}, url = {.}, abstract = {In this chapter we propose a modification of CRF-like algorithms that allows for solving large-scale structured classification problems. Our approach consists in upper bounding the CRF functional in order to decompose its training into independent optimisation problems per clique. Furthermore we show that each sub-problem corresponds to solving a multiclass learning task in each clique, which enlarges the applicability of these tools for large-scale structural learning problems. Before presenting the Conditional Graphical Model (CGM), as we refer to this procedure, we review the family of CRF algorithms. We concentrate on the best known procedures and standard generalisations of CRFs. The ob jective of this introduction is analysing from the same viewpoint the proposed solutions in the literature to tackle this problem, which allows comparing their different features. We complete the chapter with a case study, in which we show the possibility to work with large-scale problems using CGM and that the obtained performance is comparable to the result with CRF-like algorithms.} } @inproceedings{PetYuCunetal11, cat = {time}, booktitle = nips25, title = {Dynamical Segmentation of single trials from population neural data}, author = {B. Petreska and B. M. Yu and J. P. Cunningham and G. Santhanam and S. I. Ryu and K. V. Shenoy and M. Sahani}, year = 2011, address = {Granada, Spain}, month = {December}, pages = {1--8}, url = {.}, abstract = {Simultaneous recordings of many neurons embedded within a recurrently-connected cortical network may provide concurrent views into the dynamical processes of that network, and thus its computational function. In principle, these dynamics might be identified by purely unsupervised, statistical means. Here, we show that a Hidden Switching Linear Dynamical Systems (HSLDS) model - in which multiple linear dynamical laws approximate and nonlinear and potentially non-stationary dynamical process - is able to distinguish dynamical regimes within single-trial motor cortical activity associated with the preparation and initiation of hand movements. The regimes are identified without reference to behavioural or experimental epochs, but nonetheless transitions between them correlate strongly with external events whose timing may vary from trial to trial. The HSLDS model also performs better than recent comparable models in predicting the firing rate of an isolated neuron based on the firing rates of others, suggesting that it captures more of the "Shared variance" of the data. Thus, the method is able to trace the dynamical processes underlying the coordinated evolution of network activity in a way that appears to reflect its computational role.} } @article{PfiHerRas06, annote = {Winner of the 2006 Best Paper Award for the journal.}, author = {Tobias Pfingsten and Daniel Herrmann and Carl Edward Rasmussen}, journal = {IEEE Transactions on Semiconductor Manufacturing}, number = 4, pages = {475--486}, title = {Model-based design analysis and yield optimization}, url = {http://dx.doi.org/10.1109/TSM.2006.883589}, doi = {10.1109/TSM.2006.883589}, year = 2006, volume = 19, abstract = {Fluctuations are inherent to any fabrication process. Integrated circuits and microelectromechanical systems are particularly affected by these variations, and due to high-quality requirements the effect on the devices' perform ance has to be understood quantitatively. In recent years, it has become possible to model the performance of such complex systems on the basis of design specifications, and model-based sensitivity analysis has made its way into industrial engineering. We show how an efficient Bayesian approach, using a Gaussian process prior, can replace the commonly used brute-force Monte Carlo scheme, making it possible to apply the analysis to computationally costly models. We introduce a number of global, statistically justified sensitivity measures for design analysis and optimization. Two models of integrated systems serve us as case studies to introduce the analysis and to assess its convergence properties. We show that the Bayesian Monte Carlo scheme can save costly simulation runs and can ensure a reliable accuracy of the analysis.} } @inproceedings{QuiGirLarRas03, cat = {gp time}, author = {Joaquin Qui{\~n}onero-Candela and Agathe Girard and Jan Larsen and Carl Edward Rasmussen}, title = {Propagation of Uncertainty in {B}ayesian Kernel Models - Application to Multiple-Step Ahead Forecasting}, year = 2003, month = {April}, volume = 2, pages = {701--704}, journal = {IEEE International Conference on Acoustics, Speech and Signal Processing}, abstract = {The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.}, url = {.}, booktitle = {ICASSP 2003}, location = {Hong Kong} } @inproceedings{QuiGirLarRas03b, author = {Joaquin Qui{\~n}onero-Candela and Agathe Girard and Jan Larsen and Carl Edward Rasmussen}, title = {Propagation of Uncertainty in {B}ayesian Kernel Models - Application to Multiple-Step Ahead Forecasting}, year = 2003, publisher = {IEEE Press}, annote = {Electronic version of Qui{\~n}onero-Candela, Girard, Larsen and Rasmussen, 2003 which should have been presented at ICASSP 03, but was cancelled due to bird flu epidemic.}, journal = {Proceedings of 2003 IEEE International Workshop on Neural Networks for Signal Processing}, editor = {C.~Molina and T.~Adali and J.~Larsen and M.~Van Hulle and S.~C.~Douglas and J.~Rouat}, address = {Piscataway, New Jersey}, url = {#QuiGirLarRas03}, abstract = {The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.}, booktitle = {NNSP 2003}, location = {Toulouse} } @techreport{QuiGirRas03, cat = {gp time}, title = {Prediction at an uncertain input for {G}aussian processes and {Relevance Vector Machines} Application to multiple-step ahead time-series prediction}, author = {Joaquin Qui{\~n}onero-Candela and Agathe Girard and Carl Edward Rasmussen}, institution = {Instititute for Mathemetical Modelling, DTU}, number = {IMM-2003-18}, year = 2003, url = {.}, annote = {techreport} } @article{QuiRas05, cat = {gp approx}, author = {Joaquin Qui{\~n}onero-Candela and Carl Edward Rasmussen}, title = {A Unifying View of Sparse Approximate {G}aussian Process Regression}, journal = jmlr, year = 2005, pages = {1939--1959}, volume = 6, url = {http://jmlr.csail.mit.edu/papers/volume6/quinonero-candela05a/quinonero-candela05a.pdf}, abstract = {We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the methods are using. This allows new insights to be gained, and highlights the relationship between existing methods. It also allows for a clear theoretically justified ranking of the closeness of the known approximations to the corresponding full GPs. Finally we point directly to designs of new better sparse approximations, combining the best of the existing strategies, within attractive computational constraints.} } @incollection{QuiRas05b, cat = {gp}, author = {Joaquin Qui{\~n}onero-Candela and Carl Edward Rasmussen}, booktitle = {Switching and Learning in Feedback Systems}, title = {Analysis of Some Methods for Reduced Rank {G}aussian Process Regression}, year = 2005, publisher = {Springer}, pages = {98--127}, editor = {R.~Murray-Smith and R.~Shorten}, address = {Berlin, Heidelberg}, abstract = {While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical when the size of the training set exceeds a few thousand cases. This has motivated the recent proliferation of a number of cost-effective approximations to GPs, both for classification and for regression. In this paper we analyze one popular approximation to GPs for regression: the reduced rank approximation. While generally GPs are equivalent to infinite linear models, we show that Reduced Rank Gaussian Processes (RRGPs) are equivalent to finite sparse linear models. We also introduce the concept of degenerate GPs and show that they correspond to inappropriate priors. We show how to modify the RRGP to prevent it from being degenerate at test time. Training RRGPs consists both in learning the covariance function hyperparameters and the support set. We propose a method for learning hyperparameters for a given support set. We also review the Sparse Greedy GP (SGGP) approximation (Somla and Bartlett, 2001), which is a way of learning the support set for given hyperparameters based on approximating the posterior. We propose an alternative method to the SGGP that has better generalization capabilities. Finally we make experiments to compare the different ways of training a RRGP. We provide some Matlab code for learning RRGPs.}, url = {.} } @inproceedings{QuiRasSinetal06, author = {Joaquin Qui{\~n}onero-Candela and Carl Edward Rasmussen and Fabian Sinz and Olivier Bousquet and Bernhard Sch{\"o}lkopf}, title = {Evaluating Predictive Uncertainty Challenge}, year = 2006, publisher = {Springer}, pages = {1--27}, month = 04, volume = 3944, series = lncs, editor = {J.~Qui{\~n}onero-Candela and I.~Dagan and B.~Magnini and F.~d'Alch{\'e}{-}Buc}, address = {Berlin, Germany}, abstract = {This Chapter presents the PASCAL1 Evaluating Predictive Uncertainty Challenge, introduces the contributed Chapters by the participants who obtained outstanding results, and provides a discussion with some lessons to be learnt. The Challenge was set up to evaluate the ability of Machine Learning algorithms to provide good "probabilistic predictions", rather than just the usual "point predictions" with no measure of uncertainty, in regression and classification problems. Participants had to compete on a number of regression and classification tasks, and were evaluated by both traditional losses that only take into account point predictions and losses we proposed that evaluate the quality of the probabilistic predictions.}, booktitle = {Machine Learning Challenges. Evaluating predictive uncertainty, visual object classification and recognising tectual entailment. First PASCAL Machine Learning Challenges Workshop}, location = {Southampton, United Kingdom}, url = {.}, doi = {10.1007/11736790_1} } @incollection{QuiRasWil07, cat = {gp}, booktitle = {Large-Scale Kernel Machines}, author = {Joaquin Qui{\~n}onero-Candela and Carl Edward Rasmussen and Christopher K.~I.~Williams}, title = {Approximation Methods for {G}aussian Process Regression}, year = 2007, series = {Neural Information Processing}, publisher = mit, pages = {203--223}, month = {September}, editor = {L.~Bottou and O.~Chapelle and D.~DeCoste and J.~Weston}, address = {Cambridge, MA, USA}, abstract = {A wealth of computationally efficient approximation methods for Gaussian process regression have been recently proposed. We give a unifying overview of sparse approximations, following Qui{\~n}onero-Candela and Rasmussen (2005), and a brief review of approximate matrix-vector multiplication methods.}, URL = {.}, annote = {book} } @inproceedings{Ras00, cat = {np}, author = {Carl Edward Rasmussen}, title = {The Infinite {G}aussian Mixture Model}, booktitle = nips12, year = 2000, pages = {554--560}, url = {.}, editors = {Sara A. Solla, Todd K. Leen and Klaus-Robert M{\"u}ller}, publisher = mit, abstract = {In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the difficult problem of finding the "right" number of mixture components. Inference in the model is done using an efficient parameter-free Markov Chain that relies entirely on Gibbs sampling.} } @incollection{Ras03, cat = {gp mcmc}, author = {Carl Edward Rasmussen}, title = {{G}aussian Processes to Speed up {H}ybrid {M}onte {C}arlo for Expensive {B}ayesian Integrals}, booktitle = {Bayesian Statistics 7}, pages = {651--659}, url = {.}, publisher = oup, year = 2003, editors = {J.~M.~Bernardo and M.~J.~Bayarri and J.~O.~Berger and A.~P.~Dawid and D.~Heckerman and A.~F.~M.~Smith and M.~West}, abstract = {Hybrid Monte Carlo (HMC) is often the method of choice for computing Bayesian integrals that are not analytically tractable. However the success of this method may require a very large number of evaluations of the (un-normalized) posterior and its partial derivatives. In situations where the posterior is computationally costly to evaluate, this may lead to an unacceptable computational load for HMC. I propose to use a Gaussian Process model of the (log of the) posterior for most of the computations required by HMC. Within this scheme only occasional evaluation of the actual posterior is required to guarantee that the samples generated have exactly the desired distribution, even if the GP model is somewhat inaccurate. The method is demonstrated on a 10 dimensional problem, where 200 evaluations suffice for the generation of 100 roughly independent points from the posterior. Thus, the proposed scheme allows Bayesian treatment of models with posteriors that are computationally demanding, such as models involving computer simulation.} } @incollection{Ras04, cat = {gp review}, booktitle = {Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2 - 14, 2003, T{\"u}bingen, Germany, August 4 - 16, 2003, Revised Lectures}, author = {Carl Edward Rasmussen}, title = {Gaussian Processes in Machine Learning}, year = 2004, volume = 3176, series = lncs, publisher = {Springer-Verlag}, pages = {63--71}, annote = {Copyright by Springer, springerlink}, editor = {Olivier Bousquet and Ulrike von Luxburg and Gunnar R{\"a}tsch}, address = {Heidelberg}, url = {.}, abstract = {We give a basic introduction to Gaussian Process regression models. We focus on understanding the role of the stochastic process and how it is used to define a distribution over functions. We present the simple equations for incorporating training data and examine how to learn the hyperparameters using the marginal likelihood. We explain the practical advantages of Gaussian Process and end with conclusions and a look at the current trends in GP work.} } @inproceedings{Ras96, cat = {mcmc}, author = {Carl Edward Rasmussen}, title = {A practical {M}onte {C}arlo implementation of {B}ayesian learning}, booktitle = nips8, editors = {D.~S.~Touretzky and M.~C.~Mozer and M.~E.~Hasselmo}, pages = {598--604}, url = {.}, publisher = mit, address = {Cambridge, MA., USA}, year = 1996, abstract = {A practical method for Bayesian training of feed-forward neural networks using sophisticated Monte Carlo methods is presented and evaluated. In reasonably small amounts of computer time this approach outperforms other state-of-the-art methods on 5 datalimited tasks from real world domains.} } @phdthesis{Ras96b, cat = {gp}, author = {Carl Edward Rasmussen}, title = {Evaluation of {G}aussian Processes and other Methods for non-linear Regression}, year = 1996, url = {.}, school = {University of Toronto, Department of Computer Science}, address = {Toronto, CANADA}, abstract = {This thesis develops two Bayesian learning methods relying on Gaussian processes and a rigorous statistical approach for evaluating such methods. In these experimental designs the sources of uncertainty in the estimated generalisation performances due to both variation in training and test sets are accounted for. The framework allows for estimation of generalisation performance as well as statistical tests of significance for pairwise comparisons. Two experimental designs are recommended and supported by the DELVE software environment.
Two new non-parametric Bayesian learning methods relying on Gaussian process priors over functions are developed. These priors are controlled by hyperparameters which set the characteristic length scale for each input dimension. In the simplest method, these parameters are fit from the data using optimization. In the second, fully Bayesian method, a Markov chain Monte Carlo technique is used to integrate over the hyperparameters. One advantage of these Gaussian process methods is that the priors and hyperparameters of the trained models are easy to interpret.
The Gaussian process methods are benchmarked against several other methods, on regression tasks using both real data and data generated from realistic simulations. The experiments show that small datasets are unsuitable for benchmarking purposes because the uncertainties in performance measurements are large. A second set of experiments provide strong evidence that the bagging procedure is advantageous for the Multivariate Adaptive Regression Splines (MARS) method.
The simulated datasets have controlled characteristics which make them useful for understanding the relationship between properties of the dataset and the performance of different methods. The dependency of the performance on available computation time is also investigated. It is shown that a Bayesian approach to learning in multi-layer perceptron neural networks achieves better performance than the commonly used early stopping procedure, even for reasonably short amounts of computation time. The Gaussian process methods are shown to consistently outperform the more conventional methods.} } @proceedings{RasBueGieSch04, title = {Pattern Recognition: 26th {DAGM} Symposium}, editor = {Carl Edward Rasmussen and Heinrich H.~B{\"u}lthoff and Martin A.~Giese and Bernhard Sch{\"o}lkopf}, year = 2004, publisher = {Springer}, pages = 581, month = {August}, series = lncs, volume = 3175, address = {Berlin, Germany}, location = {T{\"u}bingen, Germany}, url = {http://dx.doi.org/10.1007/b99676}, doi = {10.1007/b99676} } @article{RasCruGhaWil09, cat = {clust bioinf}, author = {Carl Edward Rasmussen and Bernhard J.~de la Cruz and Zoubin Ghahramani and David L.~Wild}, title = {Modeling and Visualizing Uncertainty in Gene Expression Clusters Using {D}irichlet Process Mixtures}, journal = tcbb, volume = 6, number = 4, issn = {1545-5963}, pages = {615--628}, year = 2009, url = {http://dx.doi.org/10.1109/TCBB.2007.70269}, abstract = {Although the use of clustering methods has rapidly become one of the standard computational approaches in the literature of microarray gene expression data, little attention has been paid to uncertainty in the results obtained. Dirichlet process mixture (DPM) models provide a nonparametric Bayesian alternative to the bootstrap approach to modeling uncertainty in gene expression clustering. Most previously published applications of Bayesian model-based clustering methods have been to short time series data. In this paper, we present a case study of the application of nonparametric Bayesian clustering methods to the clustering of high-dimensional nontime series gene expression data using full Gaussian covariances. We use the probability that two genes belong to the same cluster in a DPM model as a measure of the similarity of these gene expression profiles. Conversely, this probability can be used to define a dissimilarity measure, which, for the purposes of visualization, can be input to one of the standard linkage algorithms used for hierarchical clustering. Biologically plausible results are obtained from the Rosetta compendium of expression profiles which extend previously published cluster analyses of this data.}, doi = {10.1109/TCBB.2007.70269} } @inproceedings{RasDei08, cat = {rl}, title = {Probabilistic Inference for Fast Learning in Control}, pages = {229--242}, booktitle = {Recent Advances in Reinforcement Learning}, publisher = {Springer-Verlag}, year = 2008, editor = {S. Girgin and M. Loth and R. Munos and P. Preux and D. Ryabko}, author = {Carl Edward Rasmussen and Marc Peter Deisenroth}, volume = 5323, series = lncs, type = {Lecture Notes in Artificial Intelligence}, month = {November}, address = {Villeneuve d'Ascq, France}, url = {.}, abstract = {We provide a novel framework for very fast model-based reinforcement learning in continuous state and action spaces. The framework requires probabilistic models that explicitly characterize their levels of confidence. Within this framework, we use flexible, non-parametric models to describe the world based on previously collected experience. We demonstrate learning on the cart-pole problem in a setting where we provide very limited prior knowledge about the task. Learning progresses rapidly, and a good policy is found after only a hand-full of iterations.}, annote = {videos and more. slides.} } @inproceedings{RasGha01, cat = {review}, author = {Carl Edward Rasmussen and Zoubin Ghahramani}, title = {{O}ccam's Razor}, booktitle = nips13, address = {Cambridge, MA, USA}, publisher = mit, editors = {T. Leen, T. G. Diettrich and V. Tresp}, pages = {294--300}, year = 2001, month = {December}, url = {.}, abstract = {The Bayesian paradigm apparently only sometimes gives rise to Occam's Razor; at other times very large models perform well. We give simple examples of both kinds of behaviour. The two views are reconciled when measuring complexity of functions, rather than of the machinery used to implement them. We analyze the complexity of functions for some linear in the parameter models that are equivalent to Gaussian Processes, and always find Occam's Razor at work.} } @inproceedings{RasGha02, cat = {gp np}, author = {Carl Edward Rasmussen and Zoubin Ghahramani}, title = {Infinite Mixtures of {G}aussian Process Experts}, booktitle = nips14, year = 2002, month = {December}, editors = {Dietterich, T. G., Becker, S. and Ghahramani, Z.}, pages = {881--888}, address = {Cambridge, MA, USA}, publisher = mit, url = {.}, abstract = {We present an extension to the Mixture of Experts (ME) model, where the individual experts are Gaussian Process (GP) regression models. Using an input-dependent adaptation of the Dirichlet Process, we implement a gating network for an infinite number of Experts. Inference in this model may be done efficiently using a Markov Chain relying on Gibbs sampling. The model allows the effective covariance function to vary with the inputs, and may handle large datasets --- thus potentially overcoming two of the biggest hurdles with GP models. Simulations show the viability of this approach.} } @inproceedings{RasGha03, cat = {gp mcmc}, author = {Carl Edward Rasmussen and Zoubin Ghahramani}, title = {Bayesian {Monte Carlo}}, booktitle = nips15, pages = {489--496}, year = 2003, month = {December}, address = {Cambridge, MA, USA}, editor = {S.~Becker and S.~Thrun and K.~Obermayer}, publisher = mit, url = {.}, abstract = {We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation of prior knowledge, such as smoothness of the integrand, into the estimation. In a simple problem we show that this outperforms any classical importance sampling method. We also attempt more challenging multidimensional integrals involved in computing marginal likelihoods of statistical models (a.k.a. partition functions and model evidences). We find that Bayesian Monte Carlo outperformed Annealed Importance Sampling, although for very high dimensional problems or problems with massive multimodality BMC may be less adequate. One advantage of the Bayesian approach to Monte Carlo is that samples can be drawn from any distribution. This allows for the possibility of active design of sample points so as to maximise information gain.} } @inproceedings{RasKus04, cat = {rl}, author = {Carl Edward Rasmussen and Malte Ku\ss}, booktitle = nips16, editor = {S. Thrun and L.K. Saul and B. Sch\"olkopf}, title = {Gaussian processes in reinforcement learning}, address = {Cambridge, MA, USA}, publisher = mit, year = 2004, month = {December}, pages = {751--759}, url = {.}, abstract = {We exploit some useful properties of Gaussian process (GP) regression models for reinforcement learning in continuous state spaces and discrete time. We demonstrate how the GP model allows evaluation of the value function in closed form. The resulting policy iteration algorithm is demonstrated on a simple problem with a two dimensional state space. Further, we speculate that the intrinsic ability of GP models to characterise distributions of functions would allow the method to capture entire distributions over future values instead of merely their expectation, which has traditionally been the focus of much of reinforcement learning.} } @manual{RasNeaHinetal96, author = {Carl Edward Rasmussen and Radford M.~Neal and Geoffrey E.~Hinton and Drew van Camp and Mike Revow and Zoubin Ghahramani and Rafal Kustra and Robert Tibshirani}, title = {The {DELVE} manual}, pages = {1--108}, year = 1996, abstract = {DELVE -- Data for Evaluating Learning in Valid Experiments -- is a collection of datasets from many sources, an environment within which this data can be used to assess the performance of methods for learning relationships from data, and a repository for the results of such experiments.}, url = {.}, annote = {The delve website.}, organizaton = {University of Toronto} } @article{RasNic10, cat = {gp}, author = {Carl Edward Rasmussen and Hannes Nickisch}, title = {{Gaussian Processes for Machine Learning (GPML) Toolbox}}, journal = jmlr, volume = 11, pages = {3011--3015}, year = 2010, month = {December}, url = {http://www.jmlr.org/papers/volume11/rasmussen10a/rasmussen10a.pdf}, abstract = {The GPML toolbox provides a wide range of functionality for Gaussian process (GP) inference and prediction. GPs are specified by mean and covariance functions; we offer a library of simple mean and covariance functions and mechanisms to compose more complex ones. Several likelihood functions are supported including Gaussian and heavy-tailed for regression as well as others suitable for classification. Finally, a range of inference methods is provided, including exact and variational inference, Expectation Propagation, and Laplace's method dealing with non-Gaussian likelihoods and FITC for dealing with large regression tasks.}, annote = {Toolbox avaiable from here. Implements algorithms from Rasmussen and Williams, 2006.} } @inproceedings{RasQui05, cat = {gp}, author = {Carl Edward Rasmussen and Joaquin Qui{\~n}onero-Candela}, title = {Healing the {R}elevance {V}ector {M}achine through Augmentation}, year = 2005, pages = {689--696}, booktitle = icml22, editor = {L.~De Raedt and S.~Wrobel}, abstract = {The Relevance Vector Machine (RVM) is a sparse approximate Bayesian kernel method. It provides full predictive distributions for test cases. However, the predictive uncertainties have the unintuitive property, that \emph{they get smaller the further you move away from the training cases}. We give a thorough analysis. Inspired by the analogy to non-degenerate Gaussian Processes, we suggest augmentation to solve the problem. The purpose of the resulting model, RVM*, is primarily to corroborate the theoretical and experimental analysis. Although RVM* could be used in practical applications, it is no longer a truly sparse model. Experiments show that sparsity comes at the expense of worse predictive distributions.}, location = {Bonn, Germany}, url = {.} } @book{RasWil06, cat = {gp}, author = {Carl Edward Rasmussen and Christopher K.~I.~Williams}, title = {Gaussian Processes for Machine Learning}, publisher = mit, pages = 272, year = 2006, url = {.}, abstract = {Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics.}, annote = {Winner of the 2009 DeGroot Prize. Book web page, chapters and entire book pdf. GPML Toolbox.} } @article{RasWil93, author = {Carl Edward Rasmussen and David J. Willshaw}, title = {Presynaptic and postsynaptic comptetition in models for the development of neuromuscular connections}, journal = {Biological Cybernetics}, publisher = {Springer}, volume = 68, number = 5, pages = {409--419}, year = 1993, url = {http://dx.doi.org/10.1007/BF00198773}, abstract = {In the establishment of connections between nerve and muscle there is an initial stage when each muscle fibre is innervated by several different motor axons. Withdrawal of connections then takes place until each fibre has contact from just a single axon. The evidence suggests that the withdrawal process involves competition between nerve terminals. We examine in formal models several types of competitive mechanism that have been proposed for this phenomenon. We show that a model which combines competition for a presynaptic resource with competition for a postsynaptic resource is superior to others. This model accounts for many anatomical and physiological findings and has a biologically plausible implementation. Intrinsic withdrawal appears to be a side effect of the competitive mechanism rather than a separate non-competitive feature. The model's capabilities are confirmed by theoretical analysis and full scale computer simulations.}, doi = {10.1007/BF00198773} } @inproceedings{RotVanMooGha10, cat = {ssl}, author = {Rotsos, C. and {Van Gael}, J. and Moore, A.W. and Ghahramani, Z.}, booktitle = {1st International Workshop on Traffic Analysis and Classification (IWCMC '10)}, keywords = {Machine Learning,Network,Semi Supervised}, mendeley-tags ={Machine Learning,Network,Semi Supervised}, title = {Traffic Classification in Information Poor Environments}, url = {.}, year = 2010, month = {July}, address = {Caen, France}, abstract = {Traffic classification using machine learning continues to be an active research area. The majority of work in this area uses \emph{off-the-shelf} machine learning tools and treats them as \emph{black-box} classifiers. This approach turns all the modelling complexity into a feature selection problem. In this paper, we build a problem-specific solution to the traffic classification problem by designing a custom probabilistic graphical model. Graphical models are a modular framework to design classifiers which incorporate domain-specific knowledge. More specifically, our solution introduces semi-supervised learning which means we learn from both labelled and unlabelled traffic flows. We show that our solution performs competitively compared to previous approaches while using less data and simpler features.} } @inproceedings{RotVanMooetal10, cat = {gm}, author = {Charalampos Rotsos and Jurgen {Van Gael} and Andrew W. Moore and Zoubin Ghahramani}, year = 2010, title = {Probabilistic Graphical Models for Semi-Supervised Traffic Classification}, booktitle = {The 6th International Wireless Communications and Mobile Computing Conference}, pages = {752--757}, address = {Caen, France}, url = {.}, abstract = {Traffic classification using machine learning continues to be an active research area. The majority of work in this area uses off-the-shelf machine learning tools and treats them as black-box classifiers. This approach turns all the modelling complexity into a feature selection problem. In this paper, we build a problem-specific solution to the traffic classification problem by designing a custom probabilistic graphical model. Graphical models are a modular framework to design classifiers which incorporate domain-specific knowledge. More specifically, our solution introduces semi-supervised learning which means we learn from both labelled and unlabelled traffic flows. We show that our solution performs competitively compared to previous approaches while using less data and simpler features.} } @inproceedings{SaaTurRas10, cat = {gp time}, author = {Yunus {Saat\c{c}i} and Ryan Turner and Carl Edward Rasmussen}, title = {Gaussian Process Change Point Models}, booktitle = icml27, pages = {927--934}, year = 2010, month = {June}, address = {Haifa, Israel}, url = {.}, abstract = {We combine Bayesian online change point detection with Gaussian processes to create a nonparametric time series model which can handle change points. The model can be used to locate change points in an online manner; and, unlike other Bayesian online change point detection algorithms, is applicable when temporal correlations in a regime are expected. We show three variations on how to apply Gaussian processes in the change point context, each with their own advantages. We present methods to reduce the computational burden of these models and demonstrate it on several real world data sets.}, annote = {poster, slides.} } @article{SavGhaGrietal10, cat = {bioinf}, author = {R. S. Savage and Z. Ghahramani and J. E. Griffin and B. de la Cruz and D. L. Wild}, year = 2010, title = {Discovering Transcriptional Modules by {Bayesian} Data Integration}, journal = {Bioinformatics}, volume = 26, pages = {i158--i167}, url = {.}, abstract = {Motivation: We present a method for directly inferring transcriptional modules (TMs) by integrating gene expression and transcription factor binding (ChIP-chip) data. Our model extends a hierarchical Dirichlet process mixture model to allow data fusion on a gene-by-gene basis. This encodes the intuition that co-expression and co-regulation are not necessarily equivalent and hence we do not expect all genes to group similarly in both datasets. In particular, it allows us to identify the subset of genes that share the same structure of transcriptional modules in both datasets.
Results: We find that by working on a gene-by-gene basis, our model is able to extract clusters with greater functional coherence than existing methods. By combining gene expression and transcription factor binding (ChIP-chip) data in this way, we are better able to determine the groups of genes that are most likely to represent underlying TMs.
Availability: If interested in the code for the work presented in this article, please contact the authors.} } @article{SavHelXuetal09, cat = {clust bioinf}, volume = 10, number = 242, pages = {1--9}, month = {August}, author = {R.~Savage and K.~A.~Heller and Y.~Xu and Zoubin Ghahramani and W.~Truman and M.~Grant and K.~Denby and D.~L.~Wild}, title = {{R/BHC}: fast {B}ayesian hierarchical clustering for microarray data}, publisher = {BioMed Central}, journal = {BMC Bioinformatics 2009}, year = 2009, url = {.}, abstract = {Background: Although the use of clustering methods has rapidly become one of the standard computational approaches in the literature of microarray gene expression data analysis, little attention has been paid to uncertainty in the results obtained.
Results: We present an R/Bioconductor port of a fast novel algorithm for Bayesian agglomerative hierarchical clustering and demonstrate its use in clustering gene expression microarray data. The method performs bottom-up hierarchical clustering, using a Dirichlet Process (infinite mixture) to model uncertainty in the data and Bayesian model selection to decide at each step which clusters to merge.
Conclusion: Biologically plausible results are presented from a well studied data set: expression profiles of \emph{A. thaliana} subjected to a variety of biotic and abiotic stresses. Our method avoids several limitations of traditional methods, for example how many clusters there should be and how to choose a principled distance metric.}, doi = {10.1186/1471-2105-10-242}, issn = {1471-2105}, pubmedid = 19660130 } @inproceedings{Sch09, title = {Function factorization using warped {G}aussian processes}, author = {Mikkel N. Schmidt}, booktitle = icml26, address = {Montr\'{e}al, QC, Canada}, pages = {921--928}, editor = {L\'{e}on Bottou and Michael Littman}, month = {June}, publisher = {Omnipress}, year = 2009, url = {.}, abstract = {We introduce a new approach to non-linear regression called function factorization, that is suitable for problems where an output variable can reasonably be modeled by a number of multiplicative interaction terms between non-linear functions of the inputs. The idea is to approximate a complicated function on a high-dimensional space by the sum of products of simpler functions on lower-dimensional subspaces. Function factorization can be seen as a generalization of matrix and tensor factorization methods, in which the data are approximated by the sum of outer products of vectors. We present a non-parametric Bayesian approach to function factorization where the priors over the factorizing functions are warped Gaussian processes, and we do inference using Hamiltonian Markov chain Monte Carlo. We demonstrate the superior predictive performance of the method on a food science data set compared to Gaussian process regression and tensor factorization using PARAFAC and GEMANOVA models.}, annote = {slides. poster. video.} } @inproceedings{Sch09b, title = {Linearly constrained {B}ayesian matrix factorization for blind source separation}, author = {Mikkel N. Schmidt}, booktitle = nips22, address = {Cambridge, MA, USA}, publisher = mit, editor = {Y. Bengio and D. Schuurmans and J. Lafferty and C. K. I. Williams and A. Culotta}, month = {December}, pages = {1624--1632}, year = 2009, url = {.}, abstract = {We present a general Bayesian approach to probabilistic matrix factorization subject to linear constraints. The approach is based on a Gaussian observation model and Gaussian priors with bilinear equality and inequality constraints. We present an efficient Markov chain Monte Carlo inference procedure based on Gibbs sampling. Special cases of the proposed model are Bayesian formulations of non-negative matrix factorization and factor analysis. The method is evaluated on a blind source separation problem. We demonstrate that our algorithm can be used to extract meaningful and interpretable features that are remarkably different from features extracted using existing related matrix factorization techniques.}, annote = {code.} } @inproceedings{SchMoh09, title = {Probabilistic non-negative tensor factorization using {M}arkov chain {M}onte {C}arlo}, author = {Mikkel N. Schmidt and Shakir Mohamed}, booktitle = {European Signal Processing Conference (EUSIPCO)}, address = {Glasgow, Scotland}, month = {August}, year = 2009, pages = {1918--1922}, url = {.}, abstract = {We present a probabilistic model for learning non-negative tensor factorizations (NTF), in which the tensor factors are latent variables associated with each data dimension. The non-negativity constraint for the latent factors is handled by choosing priors with support on the non-negative numbers. Two Bayesian inference procedures based on Markov chain Monte Carlo sampling are described: Gibbs sampling and Hamiltonian Markov chain Monte Carlo. We evaluate the model on two food science data sets, and show that the probabilistic NTF model leads to better predictions and avoids overfitting compared to existing NTF approaches.}, annote = {Rated by reviewers amongst the top 5% of the presented papers.} } @article{SchVenKnoetal11, cat = {bioinf}, author = {Cornelia Schone and Anne Venner and David A. Knowles and Mahesh M Karnani and Denis Burdakov}, title = {Dichotomous cellular properties of mouse orexin/hypocretin neurons}, url = {http://jp.physoc.org/content/early/2011/04/11/jphysiol.2011.208637.abstract}, journal = {The Journal of Physiology}, year = 2011, abstract = {Hypothalamic hypocretin/orexin (hcrt/orx) neurons recently emerged as critical regulators of sleep-wake cycles, reward-seeking, and body energy balance. However, at the level of cellular and network properties, it remains unclear whether hcrt/orx neurons are one homogenous population, or whether there are several distinct types of hcrt/orx cells. Here, we collated diverse structural and functional information about individual hcrt/orx neurons in mouse brain slices, by combining patch-clamp analysis of spike firing, membrane currents, and synaptic inputs with confocal imaging of cell shape and subsequent 3-dimensional Sholl analysis of dendritic architecture. Statistical cluster analysis of intrinsic firing properties revealed that hcrt/orx neurons fall into two distinct types. These two cell types also differ in the complexity of their dendritic arbour, the strength of AMPA and GABAA receptor-mediated synaptic drive that they receive, and the density of low-threshold, 4-aminopyridine-sensitive, transient K+ current. Our results provide quantitative evidence that, at the cellular level, the mouse hcrt/orx system is composed of two classes of neurons with different firing properties, morphologies, and synaptic input organization.} } @inproceedings{SchWinHan09, title = {Bayesian non-negative matrix factorization}, author = {Mikkel N. Schmidt and Ole Winther and Lars Kai Hansen}, booktitle = {8th International Conference on Independent Component Analysis and Signal Separation}, pages = {540--547}, publisher = {Springer}, address = {Paraty, Brazil}, series = lncs, volume = 5441, year = 2009, month = {March}, url = {.}, abstract = {We present a Bayesian treatment of non-negative matrix factorization (NMF), based on a normal likelihood and exponential priors, and derive an efficient Gibbs sampler to approximate the posterior density of the NMF factors. On a chemical brain imaging data set, we show that this improves interpretability by providing uncertainty estimates. We discuss how the Gibbs sampler can be used for model order selection by estimating the marginal likelihood, and compare with the Bayesian information criterion. For computing the maximum a posteriori estimate we present an iterated conditional modes algorithm that rivals existing state-of-the-art NMF algorithms on an image feature extraction problem.}, annote = {slides. code.} } @inproceedings{SilChuGha08, cat = {gm}, booktitle = nips20, month = {December}, title = {Hidden common cause relations in relational learning}, author = {R.~Silva and W.~Chu and Zoubin Ghahramani}, year = 2008, address = {Cambridge, MA, USA}, publisher = mit, editor = {J.~C.~Platt and D.~Koller and Y.~Singer and S.~Roweis}, pages = {1345--1352}, url = {.}, abstract = {When predicting class labels for objects within a relational database, it is often helpful to consider a model for relationships: this allows for information between class labels to be shared and to improve prediction performance. However, there are different ways by which objects can be related within a relational database. One traditional way corresponds to a Markov network structure: each existing relation is represented by an undirected edge. This encodes that, conditioned on input features, each object label is independent of other object labels given its neighbors in the graph. However, there is no reason why Markov networks should be the only representation of choice for symmetric dependence structures. Here we discuss the case when relationships are postulated to exist due to \emph{hidden common causes}. We discuss how the resulting graphical model differs from Markov networks, and how it describes different types of real-world relational processes. A Bayesian nonparametric classification model is built upon this graphical representation and evaluated with several empirical studies.}, annote = {Code at http://www.homepages.ucl.ac.uk/~ucgtrbd/code/xgp} } @article{SilGha09, cat = {gm}, volume = 10, month = {June}, author = {R. Silva and Z. Ghahramani}, title = {The hidden life of latent variables: {Bayesian} learning with mixed graph models}, publisher = {Association for Computing Machinery}, journal = jmlr, pages = {1187--1238}, year = 2009, url = {.}, abstract = {Directed acyclic graphs (DAGs) have been widely used as a representation of conditional independence in machine learning and statistics. Moreover, hidden or latent variables are often an important component of graphical models. However, DAG models suffer from an important limitation: the family of DAGs is not closed under marginalization of hidden variables. This means that in general we cannot use a DAG to represent the independencies over a subset of variables in a larger DAG. Directed mixed graphs (DMGs) are a representation that includes DAGs as a special case, and overcomes this limitation. This paper introduces algorithms for performing Bayesian inference in Gaussian and probit DMG models. An important requirement for inference is the specification of the distribution over parameters of the models. We introduce a new distribution for covariance matrices of Gaussian DMGs. We discuss and illustrate how several Bayesian machine learning tasks can benefit from the principle presented here: the power to model dependencies that are generated from hidden variables, but without necessarily modeling such variables explicitly.} } @inproceedings{SilGha09b, cat = {gm}, volume = 5, author = {R. Silva and Z. Ghahramani}, annote = {Code at http://www.homepages.ucl.ac.uk/~ucgtrbd/code/fmog-version0.zip}, note = {ISSN: 1938-7228}, booktitle = aistats12, title = {Factorial mixture of {Gaussians} and the marginal independence model}, publisher = jmlr, pages = {520--527}, year = 2009, month = {April}, address = {Clearwater Beach, FL, USA}, url = {.}, abstract = {Marginal independence constraints play an important role in learning with graphical models. One way of parameterizing a model of marginal independencies is by building a latent variable model where two independent observed variables have no common latent source. In sparse domains, however, it might be advantageous to model the marginal observed distribution directly, without explicitly including latent variables in the model. There have been recent advances in Gaussian and binary models of marginal independence, but no models with non-linear dependencies between continuous variables has been proposed so far. In this paper, we describe how to generalize the Gaussian model of marginal independencies based on mixtures, and how to learn parameters. This requires a non-standard parameterization and raises difficult non-linear optimization issues.} } @article{SilHelGhaetal10, cat = {ir bioinf}, author = {R. Silva and K. A. Heller and Z. Ghahramani and E. M. Airoldi}, year = 2010, pages = {615--644}, volume = 4, number = 2, title = {Ranking Relations Using Analogies in Biological and Information Networks}, journal = {Annals of Applied Statistics}, url = {.}, abstract = {Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects S = {A(1):B(1), A(2):B(2), ..., A(N):B(N)}, measures how well other pairs A:B fit in with the set S. Our work addresses the question: is the relation between objects A and B analogous to those relations found in S? Such questions are particularly relevant in information retrieval, where an investigator might want to search for analogous pairs of objects that match the query set of interest. There are many ways in which objects can be related, making the task of measuring analogies very challenging. Our approach combines a similarity measure on function spaces with Bayesian analysis to produce a ranking. It requires data containing features of the objects of interest and a link matrix specifying which relationships exist; no further attributes of such relationships are necessary. We illustrate the potential of our method on text analysis and information networks. An application on discovering functional interactions between pairs of proteins is discussed in detail, where we show that our approach can work in practice even if a small set of protein pairs is provided.} } @inproceedings{SinQuiBaketal04, cat = {gp}, author = {Fabian Sinz and Joaquin Qui{\~n}onero-Candela and G{\"o}khan H.~Bakir and Carl Edward Rasmussen and Matthias O.~Franz}, title = {Learning Depth From Stereo}, year = 2004, series = lncs, volume = 3175, publisher = {Springer}, pages = {245--252}, month = 09, journal = {Pattern Recognition: Proceedings of the 26th DAGM Symposium}, editor = {C.~E.~Rasmussen and H.~H.~B{\"u}lthoff and B.~Sch{\"o}lkopf and M.~A.~Giese}, address = {Berlin, Germany}, abstract = {We compare two approaches to the problem of estimating the depth of a point in space from observing its image position in two different cameras: 1.~The classical photogrammetric approach explicitly models the two cameras and estimates their intrinsic and extrinsic parameters using a tedious calibration procedure; 2.~A generic machine learning approach where the mapping from image to spatial coordinates is directly approximated by a Gaussian Process regression. Our results show that the generic learning approach, in addition to simplifying the procedure of calibration, can lead to higher depth accuracies than classical calibration although no specific domain knowledge is used.}, booktitle = {26th DAGM Symposium}, location = {T{\"u}bingen, Germany}, url = {.} } @InProceedings{SneGha05, cat = {approx}, author = {Edward Snelson and Zoubin Ghahramani}, title = {Compact Approximations to {B}ayesian Predictive Distributions}, booktitle = icml22, year = 2005, address = {Bonn, Germany}, month = {August}, URL = {http://www.gatsby.ucl.ac.uk/~snelson/Bayes_pred.pdf}, publisher = {Omnipress}, abstract = {We provide a general framework for learning precise, compact, and fast representations of the Bayesian predictive distribution for a model. This framework is based on minimizing the KL divergence between the true predictive density and a suitable compact approximation. We consider various methods for doing this, both sampling based approximations, and deterministic approximations such as expectation propagation. These methods are tested on a mixture of Gaussians model for density estimation and on binary linear classification, with both synthetic data sets for visualization and several real data sets. Our results show significant reductions in prediction time and memory footprint.} } @InCollection{SneGha06, cat = {gp}, title = {Sparse {G}aussian Processes using Pseudo-inputs}, author = {Edward Snelson and Zoubin Ghahramani}, booktitle = nips18, editor = {Y. Weiss and B. Sch\"{o}lkopf and J. Platt}, publisher = MIT, address = {Cambridge, MA}, pages = {1257--1264}, year = 2006, url = {http://www.gatsby.ucl.ac.uk/~snelson/SPGP_up.pdf}, abstract = {We present a new Gaussian process (GP) regression model whose covariance is parameterized by the the locations of M pseudo-input points, which we learn by a gradient based optimization. We take M<<N, where N is the number of real data points, and hence obtain a sparse regression method which has O(NM2) training cost and O(M2) prediction cost per test case. We also find hyperparameters of the covariance function in the same joint optimization. The method can be viewed as a Bayesian regression model with particular input dependent noise. The method turns out to be closely related to several other sparse GP approaches, and we discuss the relation in detail. We finally demonstrate its performance on some large data sets, and make a direct comparison to other sparse GP methods. We show that our method can match full GP performance with small M, i.e. very sparse solutions, and it significantly outperforms other approaches in this regime.} } @InProceedings{SneGha06b, cat = {gp}, author = {Edward Snelson and Zoubin Ghahramani}, title = {Variable noise and dimensionality reduction for sparse {G}aussian processes}, booktitle = uai22, editor = {R. Dechter and T. S. Richardson}, publisher = {AUAI Press}, year = 2006, url = {http://www.gatsby.ucl.ac.uk/~snelson/snelson_uai.pdf}, abstract = {The sparse pseudo-input {G}aussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M pseudo-inputs, thereby reducing complexity from O(N3) to O(NM2). One limitation of the SPGP is that this optimization space becomes impractically big for high dimensional data sets. This paper addresses this limitation by performing automatic dimensionality reduction. A projection of the input space to a low dimensional space is learned in a supervised manner, alongside the pseudo-inputs, which now live in this reduced space. The paper also investigates the suitability of the SPGP for modeling data with input-dependent noise. A further extension of the model is made to make it even more powerful in this regard - we learn an uncertainty parameter for each pseudo-input. The combination of sparsity, reduced dimension, and input-dependent noise makes it possible to apply GPs to much larger and more complex data sets than was previously practical. We demonstrate the benefits of these methods on several synthetic and real world problems.} } @InProceedings{SneGha07, cat = {gp}, author = {Edward Snelson and Zoubin Ghahramani}, title = {Local and global sparse {G}aussian process approximations}, booktitle = aistats11, editor = {M. Meila and X. Shen}, publisher = {Omnipress}, year = 2007, url = {http://www.gatsby.ucl.ac.uk/~snelson/localGP.pdf}, abstract = {{G}aussian process (GP) models are flexible probabilistic nonparametric models for regression, classification and other tasks. Unfortunately they suffer from computational intractability for large data sets. Over the past decade there have been many different approximations developed to reduce this cost. Most of these can be termed global approximations, in that they try to summarize all the training data via a small set of support points. A different approach is that of local regression, where many local experts account for their own part of space. In this paper we start by investigating the regimes in which these different approaches work well or fail. We then proceed to develop a new sparse GP approximation which is a combination of both the global and local approaches. Theoretically we show that it is derived as a natural extension of the framework developed by Qui{\~n}onero-Candela and Rasmussen for sparse GP approximations. We demonstrate the benefits of the combined approximation on some 1D examples for illustration, and on some large real-world data sets.} } @inproceedings{SneRasGha04, cat = {gp}, author = {Edward Snelson and Carl Edward Rasmussen and Zoubin Ghahramani}, title = {Warped {G}aussian Processes}, booktitle = nips16, pages = {337--344}, year = 2004, month = {December}, editor = {S.~Thrun and L.~Saul and B.~Sch{\"o}lkopf}, address = {Cambridge, MA, USA}, publisher = mit, isbn = {0-262-20152-6}, url = {.}, abstract = {We generalise the Gaussian process (GP) framework for regression by learning a nonlinear transformation of the GP outputs. This allows for non-Gaussian processes and non-Gaussian noise. The learning algorithm chooses a nonlinear transformation such that transformed data is well-modelled by a GP. This can be seen as including a preprocessing transformation as an integral part of the probabilistic modelling problem, rather than as an ad-hoc step. We demonstrate on several real regression problems that learning the transformation can lead to significantly better performance than using a regular GP, or a GP with a fixed transformation.} } @inproceedings{SolMurLeietal03, cat = {gp}, author = {Ercan Solak and Roderick Murray-Smith and William E.~Leithead and Douglas Leith and Carl Edward Rasmussen}, title = {Derivative observations in {G}aussian Process models of dynamic systems}, booktitle = nips15, pages = {1033--1040}, month = {December}, year = 2003, address = {Cambridge, MA, USA}, editor = {S.~Becker and S.~Thrun and K.~Obermayer}, publisher = mit, url = {.}, abstract = {Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data. 1) It allows us to combine derivative information, and associated uncertainty with normal function observations into the learning and inference process. This derivative information can be in the form of priors specified by an expert or identified from perturbation data close to equilibrium. 2) It allows a seamless fusion of multiple local linear models in a consistent manner, inferring consistent models and ensuring that integrability constraints are met. 3) It improves dramatically the computational efficiency of Gaussian process models for dynamic system identification, by summarising large quantities of near-equilibrium data by a handful of linearisations, reducing the training set size - traditionally a problem for Gaussian process models.} } @article{SonBraOngetal07, cat = {review}, author = {S{\"o}ren Sonnenburg and Mikio L.~Braun and Cheng Soon Ong and Samy Bengio and Leon Bottou and Geoffrey Holmes and Yann LeCun and Klaus-Robert M{\"u}ller and Fernando Pereira and Carl Edward Rasmussen and Gunnar R{\"a}tsch and Bernhard Sch{\"o}lkopf and Alexander Smola and Pascal Vincent and Jason Weston and Robert C.~Williamson}, title = {The Need for Open Source Software in Machine Learning}, year = 2007, volume = 8, pages = {2443--2466}, month = {October}, journal = jmlr, abstract = {Open source tools have recently reached a level of maturity which makes them suitable for building large-scale real-world systems. At the same time, the field of machine learning has developed a large body of powerful learning algorithms for diverse applications. However, the true potential of these methods is not realized, since existing implementations are not openly shared, resulting in software with low usability, and weak interoperability. We argue that this situation can be significantly improved by increasing incentives for researchers to publish their software under an open source model. Additionally, we outline the problems authors are faced with when trying to publish algorithmic implementations of machine learning methods. We believe that a resource of peer reviewed software accompanied by short articles would be highly valuable to both the machine learning and the general scientific community.}, url = {http://www.jmlr.org/papers/volume8/sonnenburg07a/sonnenburg07a.pdf} } @article{SteDenCooetal10, cat = {bioinf}, author = {O. Stegle and K. J. Denby and E. J. Cooke and D. L. Wild and Z. Ghahramani and K. M. Borgwardt}, year = 2010, title = {A robust {Bayesian} two-sample test for detecting intervals of differential gene expression in microarray time series}, journal = {Journal of Computational Biology}, volume = 17, number = 3, pages = {1--13}, doi = {10.1089/cmb.2009.0175}, url = {http://www.liebertonline.com/doi/abs/10.1089/cmb.2009.0175}, abstract = {Understanding the regulatory mechanisms that are responsible for an organism's response to environmental change is an important issue in molecular biology. A first and important step towards this goal is to detect genes whose expression levels are affected by altered external conditions. A range of methods to test for differential gene expression, both in static as well as in time-course experiments, have been proposed. While these tests answer the question \emph{whether} a gene is differentially expressed, they do not explicitly address the question \emph{when} a gene is differentially expressed, although this information may provide insights into the course and causal structure of regulatory programs. In this article, we propose a twosample test for identifying intervals of differential gene expression in microarray time series. Our approach is based on Gaussian process regression, can deal with arbitrary numbers of replicates, and is robust with respect to outliers. We apply our algorithm to study the response of \emph{Arabidopsis thaliana} genes to an infection by a fungal pathogen using a microarray time series dataset covering 30,336 gene probes at 24 observed time points. In classification experiments, our test compares favorably with existing methods and provides additional insights into time-dependent differential expression.} } @inproceedings{SteDenMcHetal09, cat = {bioinf time}, booktitle = {German Conference on Bioinformatics}, title = {Discovering temporal patterns of differential gene expression in microarray time series}, author = {O. Stegle and K. Denby and S. McHattie and A. Meade and D. Wild and Z. Ghahramani and K Borgwardt}, year = 2009, month = {September}, address = {Halle, Germany}, pages = {133--142}, url = {.}, abstract = {A wealth of time series of microarray measurements have become available over recent years. Several two-sample tests for detecting differential gene expression in these time series have been defined, but they can only answer the question \emph{whether} a gene is differentially expressed across the whole time series, not \emph{in which intervals} it is differentially expressed. In this article, we propose a Gaussian process based approach for studying these dynamics of differential gene expression. In experiments on \emph{Arabidopsis thaliana} gene expression levels, our novel technique helps us to uncover that the family of WRKY transcription factors appears to be involved in the early response to infection by a fungal pathogen.} } @inproceedings{SteDenWiletal09, cat = {bioinf}, booktitle = {13th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2009)}, title = {A robust {Bayesian} two-sample test for detecting intervals of differential gene expression in microarray time series}, author = {O.~Stegle and K.~Denby and David L.~Wild and Zoubin Ghahramani and Karsten Borgwardt}, year = 2009, pages = {201--216}, address = {Tucson, AZ, USA}, publisher = {Springer-Verlag}, series = {Lecture Notes in Bioinformatics}, volume = 5541, isbn = {978-3-642-02007-0}, doi = {10.1007/978-3-642-02008-7_14}, url = {.}, abstract = {Understanding the regulatory mechanisms that are responsible for an organism's response to environmental changes is an important question in molecular biology. A first and important step towards this goal is to detect genes whose expression levels are affected by altered external conditions. A range of methods to test for differential gene expression, both in static as well as in time-course experiments, have been proposed. While these tests answer the question \emph{whether} a gene is differentially expressed, they do not explicitly address the question \emph{when} a gene is differentially expressed, although this information may provide insights into the course and causal structure of regulatory programs. In this article, we propose a two-sample test for identifying \emph{intervals} of differential gene expression in microarray time series. Our approach is based on Gaussian process regression, can deal with arbitrary numbers of replicates and is robust with respect to outliers. We apply our algorithm to study the response of \emph{Arabidopsis thaliana} genes to an infection by a fungal pathogen using a microarray time series dataset covering 30,336 gene probes at 24 time points. In classification experiments our test compares favorably with existing methods and provides additional insights into time-dependent differential expression.} } @inproceedings{SteGhaGoretal09, cat = {np time}, volume = 5, month = {April}, author = {T. Stepleton and Z. Ghahramani and G.~Gordon and T.-S.~Lee}, note = {ISSN 1938-7228}, booktitle = aistats12, editor = {D. van Dyk and M. Welling}, title = {The block diagonal infinite hidden {M}arkov model}, publisher = {Microtome Publishing (paper) Journal of Machine Learning Research}, year = 2009, pages = {552--559}, address = {Clearwater Beach, FL, USA}, url = {.}, abstract = {The Infinite Hidden Markov Model (IHMM) extends hidden Markov models to have a countably infinite number of hidden states (Beal et al., 2002; Teh et al., 2006). We present a generalization of this framework that introduces nearly block-diagonal structure in the transitions between the hidden states, where blocks correspond to "sub-behaviors" exhibited by data sequences. In identifying such structure, the model classifies, or partitions, sequence data according to these sub-behaviors in an unsupervised way. We present an application of this model to artificial data, a video gesture classification task, and a musical theme labeling task, and show that components of the model can also be applied to graph segmentation.} } @article{SunGhaBan08, cat = {approx}, volume = 30, number = 12, month = {November}, author = {J.M. Sung and Z. Ghahramani and S.Y. Bang}, title = {Latent space variational {Bayes}}, publisher = {IEEE}, year = 2008, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, pages = {2236--2242}, url = {.}, abstract = {Variational Bayesian Expectation-Maximization (VBEM), an approximate inference method for probabilistic models based on factorizing over latent variables and model parameters, has been a standard technique for practical Bayesian inference. In this paper, we introduce a more general approximate inference framework for conjugate-exponential family models, which we call Latent-Space Variational Bayes (LSVB). In this approach, we integrate out the model parameters in an exact way, leaving only the latent variables. It can be shown that the LSVB approach gives better estimates of the model evidence as well as the distribution over the latent variables than the VBEM approach, but, in practice, the distribution over the latent variables has to be approximated. As a practical implementation, we present a First-order LSVB (FoLSVB) algorithm to approximate the distribution over the latent variables. From this approximate distribution, one can also estimate the model evidence and the posterior over the model parameters. The FoLSVB algorithm is directly comparable to the VBEM algorithm and has the same computational complexity. We discuss how LSVB generalizes the recently proposed collapsed variational methods to general conjugate-exponential families. Examples based on mixtures of Gaussians and mixtures of Bernoullis with synthetic and real-world data sets are used to illustrate some advantages of our method over VBEM.} } @article{SunGhaBan08b, cat = {approx}, volume = 15, month = {December}, author = {J.M. Sung and Z. Ghahramani and S.Y. Bang}, title = {Second-order latent space variational {Bayes} for approximate {B}ayesian inference}, publisher = {IEEE}, journal = {IEEE Signal Processing Letters}, pages = {918--921}, year = 2008, url = {.}, abstract = {In this letter, we consider a variational approximate Bayesian inference framework, latent-space variational Bayes (LSVB), in the general context of conjugate-exponential family models with latent variables. In the LSVB approach, we integrate out model parameters in an exact way and then perform the variational inference over only the latent variables. It can be shown that LSVB can achieve better estimates of the model evidence as well as the distribution over the latent variables than the popular variational Bayesian expectation-maximization (VBEM). However, the distribution over the latent variables in LSVB has to be approximated in practice. As an approximate implementation of LSVB, we propose a second-order LSVB (SoLSVB) method. In particular, VBEM can be derived as a special case of a first-order approximation in LSVB. SoLSVB can capture higher order statistics neglected in VBEM and can therefore achieve a better approximation. Examples of Gaussian mixture models are used to illustrate the comparison between our method and VBEM, demonstrating the improvement.} } @inproceedings{TurBotGha10, cat = {time}, author = {Ryan Turner and Steven Bottone and Zoubin Ghahramani}, title = {Fast Online Anomaly Detection Using Scan Statistics}, booktitle = {Machine Learning for Signal Processing (MLSP 2010)}, year = 2010, address = {Kittil\"{a}, Finland}, month = {August}, pages = {385--390}, isbn = {978-1-4244-7876-7}, editor = {Samuel Kaski and David J. Miller and Erkki Oja and Antti Honkela}, abstract = {We present methods to do fast online anomaly detection using scan statistics. Scan statistics have long been used to detect statistically significant bursts of events. We extend the scan statistics framework to handle many practical issues that occur in application: dealing with an unknown background rate of events, allowing for slow natural changes in background frequency, the inverse problem of finding an unusual lack of events, and setting the test parameters to maximize power. We demonstrate its use on real and synthetic data sets with comparison to other methods.}, url = {.} } @inproceedings{TurDeiRas09, cat = {gp time}, author = {Ryan Turner and Marc Peter Deisenroth and Carl Edward Rasmussen}, title = {System Identification in {G}aussian Process Dynamical Systems}, booktitle = {NIPS Workshop on Nonparametric Bayes}, year = 2009, editor = {Dilan G\"or\"ur}, address = {Whistler, BC, Canada}, month = {December}, url = {.}, annote = {poster.} } @inproceedings{TurDeiRas10, cat = {gp time}, author = {Ryan Turner and Marc Peter Deisenroth and Carl Edward Rasmussen}, title = {State-Space Inference and Learning with {G}aussian Processes}, booktitle = aistats13, year = 2010, editor = {Yee Whye Teh and Mike Titterington}, volume = 9, series = {W\&CP}, pages = {868--875}, address = {Chia Laguna, Sardinia, Italy}, month = {May 13--15}, organization = jmlr, abstract = {State-space inference and learning with Gaussian processes (GPs) is an unsolved problem. We propose a new, general methodology for inference and learning in nonlinear state-space models that are described probabilistically by non-parametric GP models. We apply the expectation maximization algorithm to iterate between inference in the latent state-space and learning the parameters of the underlying GP dynamics model.}, url = {.}, annote = {poster.} } @inproceedings{TurRas10, cat = {gp time}, author = {Ryan Turner and Carl Edward Rasmussen}, title = {Model Based Learning of Sigma Points in Unscented {K}alman Filtering}, booktitle = {Machine Learning for Signal Processing (MLSP 2010)}, year = 2010, address = {Kittil\"{a}, Finland}, pages = {178--183}, month = {August}, isbn = {978-1-4244-7876-7}, editor = {Samuel Kaski and David J. Miller and Erkki Oja and Antti Honkela}, abstract = {The unscented Kalman filter (UKF) is a widely used method in control and time series applications. The UKF suffers from arbitrary parameters necessary for a step known as sigma point placement, causing it to perform poorly in nonlinear problems. We show how to treat sigma point placement in a UKF as a learning problem in a model based view. We demonstrate that learning to place the sigma points correctly from data can make sigma point collapse much less likely. Learning can result in a significant increase in predictive performance over default settings of the parameters in the UKF and other filters designed to avoid the problems of the UKF, such as the GP-ADF. At the same time, we maintain a lower computational complexity than the other methods. We call our method UKF-L.}, url = {.} } @inproceedings{TurSaaRas09, cat = {time}, author = {Ryan Turner and Yunus Saat\c{c}i and Carl Edward Rasmussen}, title = {Adaptive Sequential {B}ayesian Change Point Detection}, booktitle = {NIPS Workshop on Temporal Segmentation}, year = 2009, editor = {Za\"{i}d Harchaoui}, address = {Whistler, BC, Canada}, month = {December}, abstract = {Real-world time series are often nonstationary with respect to the parameters of some underlying prediction model (UPM). Furthermore, it is often desirable to adapt the UPM to incoming regime changes as soon as possible, necessitating sequential inference about change point locations. A Bayesian algorithm for online change point detection (BOCPD) has been introduced recently by Adams and MacKay (2007). In this algorithm, uncertainty about the last change point location is updated sequentially, and is integrated out to make online predictions robust to parameter changes. BOCPD requires a set of fixed hyper-parameters which allow the user to fully specify the hazard function for change points and the prior distribution over the parameters of the UPM. In practice, finding the "right" hyper-parameters can be quite difficult. We therefore extend BOCPD by introducing hyper-parameter learning, without sacrificing the online nature of the algorithm. Hyper-parameter learning is performed by optimizing the marginal likelihood of the BOCPD model, a closed-form quantity which can be computed sequentially. We illustrate performance on three real-world datasets.}, url = {.}, annote = {poster, slides.} } @inproceedings{VanSaaTehGha08, cat = {np mcmc time}, abstract = {The infinite hidden Markov model is a non-parametric extension of the widely used hidden Markov model. Our paper introduces a new inference algorithm for the infinite Hidden Markov model called beam sampling. Beam sampling combines slice sampling, which limits the number of states considered at each time step to a finite number, with dynamic programming, which samples whole state trajectories efficiently. Our algorithm typically outperforms the Gibbs sampler and is more robust. We present applications of iHMM inference using the beam sampler on changepoint detection and text prediction problems.}, address = {Helsinki, Finland}, author = {Jurgen {Van Gael} and Yunus Saat\c{c}i and Yee-Whye Teh and Zoubin Ghahramani}, booktitle = icml25, pages = {1088--1095}, publisher = {ACM}, title = {Beam sampling for the infinite hidden {M}arkov model}, url = {.}, volume = 25, year = 2008 } @inproceedings{VanTehGha08, cat = {np time}, author = {{Van Gael}, J. and Teh, Y.W. and Ghahramani, Z.}, booktitle = nips21, editor = {Koller, D. and Schuurmans, D. and Bottou, L. and Bengio, Y.}, pages = {1697--1704}, address = {Cambridge, MA, USA}, publisher = mit, title = {The infinite factorial hidden {M}arkov model}, url = {.}, volume = 21, year = 2008, month = {December}, abstract = {The infinite factorial hidden Markov model is a non-parametric extension of the factorial hidden Markov model. Our model defines a probability distribution over an infinite number of independent binary hidden Markov chains which together produce an observable sequence of random variables. Central to our model is a new type of non-parametric prior distribution inspired by the Indian Buffet Process which we call the \emph{Indian Buffet Markov Process}.} } @inproceedings{VanVlaGha09, cat = {np}, author = {{Van Gael}, J. and Vlachos, A. and Ghahramani, Z.}, booktitle = {Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing (EMNLP)}, title = {The infinite {HMM} for unsupervised {PoS} tagging}, pages = {678--687}, isbn = {978-1-932432-62-6}, url = {.}, year = 2009, month = {August}, publisher = {Association for Computational Linguistics}, address = {Singapore}, abstract = {We extend previous work on fully unsupervised part-of-speech tagging. Using a non-parametric version of the HMM, called the infinite HMM (iHMM), we address the problem of choosing the number of hidden states in unsupervised Markov models for PoS tagging. We experiment with two non-parametric priors, the Dirichlet and Pitman-Yor processes, on the Wall Street Journal dataset using a parallelized implementation of an iHMM inference algorithm. We evaluate the results with a variety of clustering evaluation metrics and achieve equivalent or better performances than previously reported. Building on this promising result we evaluate the output of the unsupervised PoS tagger as a direct replacement for the output of a fully supervised PoS tagger for the task of shallow parsing and compare the two evaluations.} } @inproceedings{VanZhu07, author = {{Van Gael}, J. and Zhu, X.}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, title = {Correlation clustering for crosslingual link detection}, url = {.}, pages = {1744--1749}, year = 2007, month = {January}, address = {Hyderabad, India}, editor = {Manuela M. Veloso}, abstract = {The crosslingual link detection problem calls for identifying news articles in multiple languages that report on the same news event. This paper presents a novel approach based on constrained clustering. We discuss a general way for constrained clustering using a recent, graph-based clustering framework called correlation clustering. We introduce a correlation clustering implementation that features linear program chunking to allow processing larger datasets. We show how to apply the correlation clustering algorithm to the crosslingual link detection problem and present experimental results that show correlation clustering improves upon the hierarchical clustering approaches commonly used in link detection, and, hierarchical clustering approaches that take constraints into account.} } @inproceedings{VlaGhaBri10, cat = {clust}, author = {Andreas Vlachos and Zoubin Ghahramani and Ted Briscoe}, year = 2010, title = {Active Learning for Constrained {Dirichlet} Process Mixture Models}, booktitle = {Proceedings of the 2010 Workshop on Geometrical Models of Natural Language Semantics}, pages = {57--61}, address = {Uppsala, Sweden}, url = {.}, abstract = {Recent work applied Dirichlet Process Mixture Models to the task of verb clustering, incorporating supervision in the form of must-links and cannot-links constraints between instances. In this work, we introduce an active learning approach for constraint selection employing uncertainty-based sampling. We achieve substantial improvements over random selection on two datasets.} } @inproceedings{VlaGhaKor08, cat = {clust}, booktitle = {ICML Workshop on Prior Knowledge for Text and Language Processing}, title = {{D}irichlet process mixture models for verb clustering}, author = {A. Vlachos and Z. Ghahramani and A Korhonen}, year = 2008, month = {July}, address = {Helsinki, Finland}, pages = {43--48}, editor = {Guillaume Bouchard and Hal {Daum\'{e} III} and Marc Dymetman and Yee Whye Teh}, url = {.}, abstract = {In this work we apply Dirichlet Process Mixture Models to a learning task in natural language processing (NLP): lexical-semantic verb clustering. We assess the performance on a dataset based on Levin's (1993) verb classes using the recently introduced V-measure metric. In, we present a method to add human supervision to the model in order to to influence the solution with respect to some prior knowledge. The quantitative evaluation performed highlights the benefits of the chosen method compared to previously used clustering approaches.} } @inproceedings{VlaKorGha09, cat = {clust np}, booktitle = {4th Workshop on Statistical Machine Translation, EACL '09}, title = {Unsupervised and constrained {Dirichlet} process mixture models for verb clustering}, author = {A. Vlachos and A Korhonen and Z. Ghahramani}, year = 2009, month = {March}, address = {Athens, Greece}, url = {.}, abstract = {In this work, we apply Dirichlet Process Mixture Models (DPMMs) to a learning task in natural language processing (NLP): lexical-semantic verb clustering. We thoroughly evaluate a method of guiding DPMMs towards a particular clustering solution using pairwise constraints. The quantitative and qualitative evaluation performed highlights the benefits of both standard and constrained DPMMs compared to previously used approaches. In addition, it sheds light on the use of evaluation measures and their practical application.} } @inproceedings{WilGha08, author = {Sinead Williamson and Zoubin Ghahramani}, year = 2008, title = {Probabilistic Models for Data Combination in Recommender Systems}, booktitle = {Learning from Multiple Sources Workshop, NIPS Conference}, address = {Whistler Canada}, url = {.} } @inproceedings{WilGha10, cat = {np gp time}, author = {Andrew Gordon Wilson and Zoubin Ghahramani}, title = {Copula Processes}, booktitle = nips23, year = 2010, abstract = {We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures. }, url = {http://books.nips.cc/papers/files/nips23/NIPS2010_0784.pdf}, annote = {Supplementary Material, slides.}, note = {Spotlight} } @inproceedings{WilGha11, cat = {np gp time}, author = {Andrew Gordon Wilson and Zoubin Ghahramani}, title = {Generalised {W}ishart Processes}, booktitle = uai27, year = 2011, abstract = {We introduce a new stochastic process called the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary input variable. We use this process as a prior over dynamic (e.g. time varying) covariance matrices. The GWP captures a diverse class of covariance dynamics, naturally hanles missing data, scales nicely with dimension, has easily interpretable parameters, and can use input variables that include covariates other than time. We describe how to construct the GWP, introduce general procedures for inference and prediction, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. }, url = {http://uai.sis.pitt.edu/papers/11/p736-wilson.pdf}, annote = {Supplementary Material, Best Student Paper Award} } @techreport{WilKnoGha11, cat = {np gp time}, author = {Andrew Gordon Wilson and David A Knowles and Zoubin Ghahramani}, title = {Gaussian Process Regression Networks}, number = {arXiv:1110.4411 [stat.ML]}, institution = {Department of Engineering, University of Cambridge}, address = {Cambridge, UK}, abstract = {We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables, input dependent length-scales and amplitudes, and heavy-tailed predictive distributions. We derive both efficient Markov chain Monte Carlo and variational Bayes inference procedures for this model. We apply GPRN as a multiple output regression and multivariate volatility model, demonstrating substantially improved performance over eight popular multiple output (multi-task) Gaussian process models and three multivariate volatility models on benchmark datasets, including a 1000 dimensional gene expression dataset. }, month = {October 19}, year = 2011, url = {.}, annote = {arXiv:1110.4411} } @inproceedings{WilOrbGha10, cat = {np}, author = {Sinead Williamson and Peter Orbanz and Zoubin Ghahramani}, title = {Dependent {I}ndian buffet processes}, booktitle = aistats13, year = 2010, volume = 9, series = {W\&CP}, address = {Chia Laguna, Sardinia, Italy}, month = {May}, pages = {924--931}, url = {.}, abstract = {Latent variable models represent hidden structure in observational data. To account for the distribution of the observational data changing over time, space or some other covariate, we need generalizations of latent variable models that explicitly capture this dependency on the covariate. A variety of such generalizations has been proposed for latent variable models based on the Dirichlet process. We address dependency on covariates in binary latent feature models, by introducing a dependent Indian Buffet Process. The model generates a binary random matrix with an unbounded number of columns for each value of the covariate. Evolution of the binary matrices over the covariate set is controlled by a hierarchical Gaussian process model. The choice of covariance functions controls the dependence structure and exchangeability properties of the model. We derive a Markov Chain Monte Carlo sampling algorithm for Bayesian inference, and provide experiments on both synthetic and real-world data. The experimental results show that explicit modeling of dependencies significantly improves accuracy of predictions.} } @inproceedings{WilRas96, cat = {gp}, author = {Chris K.~I.~Williams and Carl Edward Rasmussen}, title = {Gaussian processes for regression}, booktitle = nips8, editors = {D.~S.~Touretzky and M.~C.~Mozer and M.~E.~Hasselmo}, pages = {514--520}, publisher = mit, address = {Cambridge, MA., USA}, abstract = {The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior over functions. We investigate the use of a Gaussian process prior over functions, which permits the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations. Two methods, using optimization and averaging (via Hybrid Monte Carlo) over hyperparameters have been tested on a number of challenging problems and have produced excellent results.}, year = 1996, url = {.} } @techreport{WilRasSchTre02, cat = {gp}, author = {Christopher K.~I.~Williams and Carl Edward Rasmussen and Anton Schwaighofer and Volker Tresp}, title = {Observations on the {N}ystr{\"o}m Method for {G}aussian Process Prediction}, url = {.}, year = 2002, institution = {University of Edinburgh}, abstract = {A number of methods for speeding up Gaussian Process (GP) prediction have been proposed, including the Nystr{\"o}m method of Williams and Seeger (2001). In this paper we focus on two issues (1) the relationship of the Nystr{\"o}m method to the Subset of Regressors method (Poggio and Girosi 1990; Luo and Wahba, 1997) and (2) understanding in what circumstances the Nystr{\"o}m approximation would be expected to provide a good approximation to exact GP regression.} } @inproceedings{WilWanHelBle10, cat = {np}, author = {Sinead Williamson and Katherine A. Heller and C. Wang and D. M. Blei}, title = {The {IBP} compound {D}irichlet process and its application to focused topic modeling}, booktitle = icml27, pages = {1151--1158}, year = 2010, month = {June}, address = {Haifa, Israel}, url = {.}, abstract = {The hierarchical Dirichlet process (HDP) is a Bayesian nonparametric mixed membership model --- each data point is modeled with a collection of components of different proportions. Though powerful, the HDP makes an assumption that the probability of a component being exhibited by a data point is positively correlated with its proportion within that data point. This might be an undesirable assumption. For example, in topic modeling, a topic (component) might be rare throughout the corpus but dominant within those documents (data points) where it occurs. We develop the IBP compound Dirichlet process (ICD), a Bayesian nonparametric prior that decouples across-data prevalence and within-data proportion in a mixed membership model. The ICD combines properties from the HDP and the Indian buffet process (IBP), a Bayesian nonparametric prior on binary matrices. The ICD assigns a subset of the shared mixture components to each data point. This subset, the data point's "focus", is determined independently from the amount that each of its components contribute. We develop an ICD mixture model for text, the focused topic model (FTM), and show superior performance over the HDP-based topic model.} } @inproceedings{XuHelGha09, cat = {np approx}, volume = 5, author = {Yang Xu and Katherine A. Heller and Zoubin Ghahramani}, note = {ISSN 1938-7228}, booktitle = aistats12, editor = {D.~van Dyk and M.~Welling}, title = {Tree-based inference for {D}irichlet process mixtures}, publisher = {Microtome Publishing (paper), Journal of Machine Learning Research (online)}, year = 2009, month = {April}, address = {Clearwater Beach, FL, USA}, pages = {623--630}, url = {.}, abstract = {The Dirichlet process mixture (DPM) is a widely used model for clustering and for general nonparametric Bayesian density estimation. Unfortunately, like in many statistical models, exact inference in a DPM is intractable, and approximate methods are needed to perform efficient inference. While most attention in the literature has been placed on Markov chain Monte Carlo (MCMC) [1, 2, 3], variational Bayesian (VB) [4] and collapsed variational methods [5], [6] recently introduced a novel class of approximation for DPMs based on Bayesian hierarchical clustering (BHC). These tree-based combinatorial approximations efficiently sum over exponentially many ways of partitioning the data and offer a novel lower bound on the marginal likelihood of the DPM [6]. In this paper we make the following contributions: (1) We show empirically that the BHC lower bounds are substantially tighter than the bounds given by VB [4] and by collapsed variational methods [5] on synthetic and real datasets. (2) We also show that BHC offers a more accurate predictive performance on these datasets. (3) We further improve the tree-based lower bounds with an algorithm that efficiently sums contributions from alternative trees. (4) We present a fast approximate method for BHC. Our results suggest that our combinatorial approximate inference methods and lower bounds may be useful not only in DPMs but in other models as well.} } @article{YuCunSanetal09a, cat = {gp}, author = {B. M. Yu and J. P. Cunningham and G. Santhanam and S. I. Ryu and K. V. Shenoy and M. Sahani}, title = {{G}aussian-process factor analysis for low-dimensional single-trial analysis of neural population activity}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/YuJNP2009.pdf}, journal = {Journal of Neurophysiology}, volume = 102, pages = {614-635}, year = 2009, abstract = {We consider the problem of extracting smooth, low-dimensional neural trajectories that summarize the activity recorded simultaneously from many neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional, noisy spiking activity in a compact form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the spike trains are first smoothed over time, then a static dimensionality- reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way and that account for spiking variability, which may vary both across neurons and across time. We then present a novel method for extracting neural trajectories -- Gaussian-process factor analysis (GPFA) -- which unifies the smoothing and dimensionality- reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that the proposed extensions improved the predictive ability of the two-stage methods. The predictive ability was further improved by going to GPFA. From the extracted trajectories, we directly observed a convergence in neural state during motor planning, an effect that was shown indirectly by previous studies. We then show how such methods can be a powerful tool for relating the spiking activity across a neural population to the subject's behavior on a single-trial basis. Finally, to assess how well the proposed methods characterize neural population activity when the underlying time course is known, we performed simulations that revealed that GPFA performed tens of percent better than the best two-stage method.} } @inproceedings{YuCunSanetal09b, cat = {gp}, booktitle = nips21, author = {B. M. Yu and J. P. Cunningham and G. Santhanam and S. I. Ryu and K. V. Shenoy and M. Sahani}, title = {{G}aussian-process factor analysis for low-dimensional single-trial analysis of neural population activity}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/YuNIPS2009.pdf}, year = 2009, address = {Vancouver, BC}, month = {December}, pages = {1--8}, abstract = {We consider the problem of extracting smooth, low-dimensional neural trajectories that summarize the activity recorded simultaneously from many neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional, noisy spiking activity in a compact form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the spike trains are first smoothed over time, then a static dimensionality- reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way and that account for spiking variability, which may vary both across neurons and across time. We then present a novel method for extracting neural trajectories -- Gaussian-process factor analysis (GPFA) -- which unifies the smoothing and dimensionality- reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that the proposed extensions improved the predictive ability of the two-stage methods. The predictive ability was further improved by going to GPFA. From the extracted trajectories, we directly observed a convergence in neural state during motor planning, an effect that was shown indirectly by previous studies. We then show how such methods can be a powerful tool for relating the spiking activity across a neural population to the subject's behavior on a single-trial basis. Finally, to assess how well the proposed methods characterize neural population activity when the underlying time course is known, we performed simulations that revealed that GPFA performed tens of percent better than the best two-stage method.} } @article{ZhaBatCunetal11, cat = {time}, author = {M. Zhao and A. P. Batista and J. P. Cunningham and C. A. Chestek and Z. Rivera-Alvidrez and R. Kalmar and S. I. Ryu and K. V. Shenoy and S. Iyengar}, title = {An {L}1-regularized logistic model for detecting short-term neuronal interactions.}, url = {http://mlg.eng.cam.ac.uk/john/pubs/pdf/ZhaoJCNS2011.pdf}, doi = {10.1007/s10827-011-0365-5}, journal = {Journal of Computational Neuroscience}, note = {In Press.}, year = 2011, abstract = {Interactions among neurons are a key com- ponent of neural signal processing. Rich neural data sets potentially containing evidence of interactions can now be collected readily in the laboratory, but existing analysis methods are often not sufficiently sensitive and specific to reveal these interactions. Generalized linear models offer a platform for analyzing multi-electrode recordings of neuronal spike train data. Here we suggest an L1-regularized logistic regression model (L1L method) to detect short-term (order of 3ms) neuronal interactions. We estimate the parameters in this model using a coordinate descent algorithm, and determine the optimal tuning parameter using a Bayesian Information Criterion. Simulation studies show that in general the L1L method has better sensitivities and specificities than those of the traditional shuffle-corrected cross-correlogram (covariogram) method. The L1L method is able to detect excitatory interactions with both high sensitivity and specificity with reasonably large recordings, even when the magnitude of the interactions is small; similar results hold for inhibition given sufficiently high baseline firing rates. Our study also suggests that the false positives can be further removed by thresholding, because their magnitudes are typically smaller than true interactions. Simulations also show that the L1L method is somewhat robust to partially observed networks. We apply the method to multi-electrode recordings collected in the monkey dorsal premotor cortex (PMd) while the animal prepares to make reaching arm movements. The results show that some neurons interact differently depending on task conditions. The stronger interactions detected with our L1L method were also visible using the covariogram method.} } @article{ZhaGhaYan08, cat = {gm}, volume = 73, number = 3, month = {December}, author = {J. Zhang and Z. Ghahramani and Y. Yang}, title = {Flexible latent variable models for multi-task learning}, publisher = {Springer Netherlands}, year = 2008, journal = {Machine Learning}, pages = {221--242}, url = {.}, abstract = {Given multiple prediction problems such as regression and classification, we are interested in a joint inference framework which can effectively borrow information among tasks to improve the prediction accuracy, especially when the number of training examples per problem is small. In this paper we propose a probabilistic framework which can support a set of latent variable models for different multi-task learning scenarios. We show that the framework is a generalization of standard learning methods for single prediction problems and it can effectively model the shared structure among different prediction tasks. Furthermore, we present efficient algorithms for the empirical Bayes method as well as point estimation. Our experiments on both simulated datasets and real world classification datasets show the effectiveness of the proposed models in two evaluation settings: standard multi-task learning setting and transfer learning setting.} }