Statistical Approaches to Learning and Discovery Course Web Page

10-602 CALD
15-802 Computer Science
36-712 Statistics
80-802 Philosophy

Statistical Approaches to Learning and Discovery

Course Web Page

Time: Mondays and Wednesdays 1:00 pm - 2:20 pm

Location: Wean Hall 4615A

Instructors: Zoubin Ghahramani (zoubin@cs.cmu.edu) and Teddy Seidenfeld (teddy@stat.cmu.edu)

Textbook: Tanner's "Tools for Statistical Inference", supplemented by readings.

Additional Reference Material: G.Casella and R.Berger, "Statistical Inference." and J.O.Berger, "Statistical Decision Theory" 1st ed. (only). Both books are on "Reserve" in the E&S Library. The 2nd edition of Berger is better, but was not in the library yesterday. We'll try to get the 2nd ed. on reserve once it shows up.

Written Requirements: There will be approximately 5 homework assignments, a mid-term examination, and a final examination.

Tentative Topic List and Schedule

Here is a schedule of class meetings and a preliminary choice of topics to be covered.
We emphasize that the selection of topics and their order of appearance is tentative.

Week 1 (Jan 14 and 16) Introduction, information theory and statistics	Supervised vs Unsupervised vs Reinforcement Learning Statistics and Information theory Maximum Likelihood Bayesian learning	Lecture Slides
Week 2 (Jan 23) Some asymptotics of Bayesian inference	Asymptotic certainty Asymptotic consensus	Lecture Slides (corrected) Tanner Chapter 2
Week 3 (Jan 28 and 30) Normal and other approximations to Bayesian inference	Symmetry and independence assumptions Data reduction Asymptotic Normality	Tanner Chapter 2 Lecture Slides (Monday) Lecture Slides (Wednesday)
Week 4 (Feb 4 and 6) Latent variable models	Mixture of Gaussians (MoG) and k-means Factor Analysis (FA) and PCA Relation to Neural Networks	Lecture Slides(revised) Homework 1 (revised, due Wed Feb 13) Text data for Beta-binomial problem Matlab minimize function Matlab digamma function
Week 5 (Feb 11 and 13) The EM algorithm	General theory Missing data Exponential Family Bayesian and non-Bayesian form Applications to MoG and FA	Lecture Slides (Mon) Extended Remarks on Improper Priors Slide on KL Inequality Lecture Slides (Wed) Tanner Chapter 4
Week 6 (Feb 18 and 20) MCMC methods	Simple Monte Carlo Rejection Sampling Importance Sampling Gibbs Sampling Relation between Gibbs, MCMC and EM	Lecture Slides (Mon) Gibbs sampling demo (needs plot_gaussian) Tanner Chapter 6 and additional readings Lecture Slides (Wed) Radford Neal's Technical Report
Week 7 (Feb 25 and 27) MCMC methods	EM as MM, a counterexample Metropolis Hybrid Monte Carlo and other topics in sampling	EM as MM with an EM counterexample (Mon / Teddy) metropolis demos: one and two hybrid Monte Carlo demo
Week 8 (March 4 and 6) Variational Methods and Probabilistic Graphical Models	Variational Methods Conditional Independence Bayesian Networks (directed graphical models) d-Separation	Lecture Slides (Mon) Jordan et al Variational Tutorial Homework 2 (part 1) Homework 2 (part 2) Data for Hw 2: images.jpg Data generating code: genimages.m
Week 9 (March 11 and 13) Probabilistic Graphical Models and Causal Inference	Markov Networks (undirected graphical models) Hammersley-Clifford Theorem Belief Propagation Causal Inference	Lecture Slides (Mon) Lecture Slides (Scheines) [pdf] [ppt][html][html - yellow teeth] Scheines, R. An Introduction to Causal Inference. Spirtes, P., Richardson, T., Meek, C., Scheines, R., and Glymour, C. (1997). Using Path Diagrams as a Structural Equation Modelling Tool (Sociological Methods and Research) Scheines, R., Spirtes, P., Glymour, C., Meek, C., and Richardson, T. (forthcoming). The TETRAD Project: Constraint Based Aids to Causal Model Specification (Multivariate Behavioral Research) Tetrad Software Project Homepage
Week 10 /11 (March 18, 20, 25, 27) Latent Variable Time Series Models	Hidden Markov Models (HMMs) Forward-Backward and Viterbi Linear Dynamical Systems Kalman Filtering (KF) and Extended KF Particle Filters Hybrid and Nonlinear Time Series Models Dynamic Bayesian Networks	Paper on Learning Dynamic Bayesian Networks[pdf] [ps] Lecture Slides (Wed 20, Mon 25) .
CMU SPRING BREAK	.	.
Week 12 (April 8 and 10) Sample Reuse Techniques	Jackknife Bootstrap	Lecture Slides (Sample Reuse Techniques) Homework 3 (part 1) geyser.txt
Week 13/14 (April 15, 17, 22) Reinforcement Learning and Sequential Decisions	Decisions Active Learning Experiment Design Reinforcement Learning Markov Decision Problems The Bellman Equation Temporal Difference and Q-learning Relation to Optimal Control and Influence Diagrams	Lecture Slides (Sequential Decision Making) Lecture Slides (Reinforcement Learning) Sutton and Barto Textboook Kaelbling, Littman and Moore Review Paper
Week 14/15 (April 24, 29, May 1) Model Selection	Bayes Factors Multiple Testing BIC/MDL Laplace Approximation and Variational Methods Cross Validation	Lecture Slides (Bayesian Model Selection) Lecture Slides (Cross Validation)

Other topics we would have liked to cover:

Additive Models
Boosting
Iterative Scaling
AIC

Exact Sampling Methods

Hierarchical and Nonlinear Latent-Variable Models:

Independent Components Analysis (ICA)
Sigmoid Belief Networks
Boltzmann Machines

Nonparametric Inference

Kernel Methods
Density estimation, classification and regression
Gaussian processes as infinite neural networks, Bayesian kernels machines and priors over functions
Dirichlet Processes and infinite mixture models

Loopy Belief Propagation, Bethe Approximations, and Kikuchi Approximations

Expectation Propagation