Pathologies of Factorised Gaussian and MC Dropout Posteriors in Bayesian Neural Networks

Neural networks provide state-of-the-art performance on a variety of tasks. However, they are often overconfident when making predictions. This inability to properly account for uncertainty limits their application to high-risk decision making, active learning and Bayesian optimisation. To address this, Bayesian inference has been proposed as a framework for improving uncertainty estimates. In practice, Bayesian neural networks rely on poorly understood approximations for computational tractability. We prove that two commonly used approximation methods, the factorised Gaussian assumption and Monte Carlo dropout, lead to pathological estimates of the predictive uncertainty in single hidden layer ReLU networks. This indicates that more flexible approximations are needed to obtain reliable uncertainty estimates.

'In-Between' Uncertainty in Bayesian Neural Networks

We describe a limitation in the expressiveness of the predictive uncertainty estimate given by mean-field variational inference (MFVI), a popular approximate inference method for Bayesian neural networks. In particular, MFVI fails to give calibrated uncertainty estimates in between separated regions of observations. This can lead to catastrophically overconfident predictions when testing on out-of-distribution data. Avoiding such overconfidence is critical for active learning, Bayesian optimisation and out-of-distribution robustness. We instead find that a classical technique, the linearised Laplace approximation, can handle 'in-between' uncertainty much better for small network architectures.

Interpretable Outcome Prediction with Sparse Bayesian Neural Networks in Intensive Care

Clinical decision making is challenging because of pathological complexity, as well as large amounts of heterogeneous data generated as part of routine clinical care. In recent years, machine learning tools have been developed to aid this process. Intensive care unit (ICU) admissions represent the most data dense and time-critical patient care episodes. In this context, prediction models may help clinicians determine which patients are most at risk and prioritize care. However, flexible tools such as artificial neural networks (ANNs) suffer from a lack of interpretability limiting their acceptability to clinicians. In this work, we propose a novel interpretable Bayesian neural network architecture which offers both the flexibility of ANNs and interpretability in terms of feature selection. In particular, we employ a sparsity inducing prior distribution in a tied manner to learn which features are important for outcome prediction. We evaluate our approach on the task of mortality prediction using two real-world ICU cohorts. In collaboration with clinicians we found that, in addition to the predicted outcome results, our approach can provide novel insights into the importance of different clinical measurements. This suggests that our model can support medical experts in their decision making process.

Are Generative Classifiers More Robust to Adversarial Attacks?

There is a rising interest in studying the robustness of deep neural network classifiers against adversaries, with both advanced attack and defence techniques being actively developed. However, most recent work focuses on discriminative classifiers, which only model the conditional distribution of the labels given the inputs. In this paper we propose the deep Bayes classifier, which improves classical naive Bayes with conditional deep generative models. We further develop detection methods for adversarial examples, which reject inputs that have negative log-likelihood under the generative model exceeding a threshold pre-specified using training data. Experimental results suggest that deep Bayes classifiers are more robust than deep discriminative classifiers, and the proposed detection methods achieve high detection rates against many recently proposed attacks.

Disentangled Sequential Autoencoder

We present a VAE architecture for encoding and generating high dimensional sequential data, such as video or audio. Our deep generative model learns a latent representation of the data which is split into a static and dynamic part, allowing us to approximately disentangle latent time-dependent features (dynamics) from features which are preserved over time (content). This architecture gives us partial control over generating content and dynamics by conditioning on either one of these sets of features. In our experiments on artificially generated cartoon video clips and voice recordings, we show that we can convert the content of a given sequence into another one by such content swapping. For audio, this allows us to convert a male speaker into a female speaker and vice versa, while for video we can separately manipulate shapes and dynamics. Furthermore, we give empirical evidence for the hypothesis that stochastic RNNs as latent state models are more efficient at compressing and generating long sequences than deterministic ones, which may be relevant for applications in video compression.

Meta-Learning for Stochastic Gradient MCMC

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic model, even a simple modification of the underlying dynamical system requires significant physical intuition. This paper presents the first meta-learning algorithm that allows automated design for the underlying continuous dynamics of an SG-MCMC sampler. The learned sampler generalizes Hamiltonian dynamics with state-dependent drift and diffusion, enabling fast traversal and efficient exploration of neural network energy landscapes. Experiments validate the proposed approach on both Bayesian fully connected neural network and Bayesian recurrent neural network tasks, showing that the learned sampler out-performs generic, hand-designed SG-MCMC algorithms, and generalizes to different datasets and larger architectures.

Variational Implicit Processes

This paper introduces the variational implicit processes (VIPs), a Bayesian nonparametric method based on a class of highly flexible priors over functions. Similar to Gaussian processes (GPs), in implicit processes (IPs), an implicit multivariate prior (data simulators, Bayesian neural networks, etc.) is placed over any finite collections of random variables. A novel and efficient variational inference algorithm for IPs is derived using wake-sleep updates, which gives analytic solutions and allows scalable hyper-parameter learning with stochastic optimization. Experiments on real-world regression datasets demonstrate that VIPs return better uncertainty estimates and superior performance over existing inference methods for GPs and Bayesian neural networks. With a Bayesian LSTM as the implicit prior, the proposed approach achieves state-of-the-art results on predicting power conversion efficiency of molecules based on raw chemical formulas.

Variational Continual Learning

This paper develops variational continual learning (VCL), a simple but general framework for continual learning that fuses online variational inference (VI) and recent advances in Monte Carlo VI for neural networks. The framework can successfully train both deep discriminative models and deep generative models in complex continual learning settings where existing tasks evolve over time and entirely new tasks emerge. Experimental results show that VCL outperforms state-of-the-art continual learning methods on a variety of tasks, avoiding catastrophic forgetting in a fully automatic way.

Gradient Estimators for Implicit Models

Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press approximate inference techniques relying on implicit distributions. The majority of existing approaches to learning implicit models rely on approximating the intractable distribution or optimisation objective for gradient-based optimisation, which is liable to produce inaccurate updates and thus poor models. This paper alleviates the need for such approximations by proposing the Stein gradient estimator, which directly estimates the score function of the implicitly defined distribution. The efficacy of the proposed estimator is empirically demonstrated by examples that include meta-learning for approximate inference, and entropy regularised GANs that provide improved sample diversity.

Approximate Inference with Amortised MCMC

We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the approximation network thereby improving its quality. This provides a new generic framework for approximate inference, allowing us to deploy highly complex, or implicitly defined approximation families with intractable densities, including approximations produced by warping a source of randomness through a deep neural network. Experiments consider image modelling with deep generative models as a challenging test for the method. Deep models trained using amortised MCMC are shown to generate realistic looking samples as well as producing diverse imputations for images with regions of missing pixels.