I am a postdoctoral researcher at the Cambridge Machine Learning Group. My research interests lie broadly within probabilistic machine learning and statistics. Of late, I’ve been working on priors for Bayesian neural networks and critiquing deep generative models. I completed my PhD under the supervision of Padhraic Smyth at the University of California, Irvine. I’ve done research internships at DeepMind, Twitter Cortex, Microsoft Research, and Amazon.

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Publications

Adapting the Linearised Laplace Model Evidence for Modern Deep Learning

Javier Antorán, David Janz, James Urquhart Allingham, Erik A. Daxberger, Riccardo Barbano, Eric T. Nalisnick, José Miguel Hernández-Lobato, 2022. (In 39th International Conference on Machine Learning). Edited by Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvári, Gang Niu, Sivan Sabato. PMLR. Proceedings of Machine Learning Research.

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The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection. We show that these interact poorly with some now-standard tools of deep learning–stochastic approximation methods and normalisation layers–and make recommendations for how to better adapt this classic method to the modern setting. We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers.

Bayesian Deep Learning via Subnetwork Inference

Erik A. Daxberger, Eric T. Nalisnick, James Urquhart Allingham, Javier Antorán, José Miguel Hernández-Lobato, 2021. (In 32nd International Conference on Machine Learning). Edited by Marina Meila, Tong Zhang. PMLR. Proceedings of Machine Learning Research.

Abstract▼ URL

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model’s predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.

Dropout as a Structured Shrinkage Prior

Eric Nalisnick, José Miguel Hernández-Lobato, Padhraic Smyth, June 2019. (In 36th International Conference on Machine Learning). Long Beach.

Abstract▼ URL

Dropout regularization of deep neural networks has been a mysterious yet effective tool to prevent overfitting. Explanations for its success range from the prevention of co-adapted weights to it being a form of cheap Bayesian inference. We propose a novel framework for understanding multiplicative noise in neural networks, considering continuous distributions as well as Bernoulli noise (i.e. dropout). We show that multiplicative noise induces structured shrinkage priors on a network’s weights. We derive the equivalence through reparametrization properties of scale mixtures and without invoking any approximations. Given the equivalence, we then show that dropout’s Monte Carlo training objective approximates marginal MAP estimation. We leverage these insights to propose a novel shrinkage framework for resnets, terming the prior ‘automatic depth determination’ as it is the natural analog of automatic relevance determination for network depth. Lastly, we investigate two inference strategies that improve upon the aforementioned MAP approximation in regression benchmarks.

Bayesian batch active learning as sparse subset approximation

Robert Pinsler, Jonathan Gordon, Eric Nalisnick, Jose Miguel Hernández-Lobato, 2019. (In Advances in Neural Information Processing Systems 33).

Abstract▼ URL

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the most informative data points to be labeled. However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change. In this paper, we introduce a novel Bayesian batch active learning approach that mitigates these issues. Our approach is motivated by approximating the complete data posterior of the model parameters. While naive batch construction methods result in correlated queries, our algorithm produces diverse batches that enable efficient active learning at scale. We derive interpretable closed-form solutions akin to existing active learning procedures for linear models, and generalize to arbitrary models using random projections. We demonstrate the benefits of our approach on several large-scale regression and classification tasks.

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