Publications and Code

**A Unifying Bayesian View of Continual Learning**

Some machine learning applications require continual learning—where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model posterior one would simply use this as the prior for the next task. However, exact posterior evaluation is intractable with many models, especially with Bayesian neural networks (BNNs). Instead, posterior approximations are often sought. Unfortunately, when posterior approximations are used, prior-focused approaches do not succeed in evaluations designed to capture properties of realistic continual learning use cases. As an alternative to prior-focused methods, we introduce a new approximate Bayesian derivation of the continual learning loss. Our loss does not rely on the posterior from earlier tasks, and instead adapts the model itself by changing the likelihood term. We call these approaches likelihood-focused. We then combine prior- and likelihood-focused methods into one objective, tying the two views together under a single unifying framework of approximate Bayesian continual learning.

Sebastian Farquhar, Yarin Gal

**NeurIPS 2018 workshop on Bayesian Deep Learning**[Paper] [BibTex]

**On the Connection between Neural Processes and Gaussian Processes with Deep Kernels**

Neural Processes (NPs) are a class of neural latent variable models that combine desirable properties of Gaussian Processes (GPs) and neural networks. Like GPs, NPs define distributions over functions and are able to estimate the uncertainty in their predictions. Like neural networks, NPs are computationally efficient during training and prediction time. We establish a simple and explicit connection between NPs and GPs. In particular, we show that, under certain conditions, NPs are mathematically equivalent to GPs with deep kernels. This result further elucidates the relationship between GPs and NPs and makes previously derived theoretical insights about GPs applicable to NPs. Furthermore, it suggests a novel approach to learning expressive GP covariance functions applicable across different prediction tasks by training a deep kernel GP on a set of datasets

Tim G. J. Rudner, Vincent Fortuin, Yarin Gal, Yee Whye Teh

**Workshop on Bayesian Deep Learning, NeurIPS 2018**[Paper] [BibTex]

**Targeted Dropout**

Neural networks are extremely flexible models due to their large number of parameters, which is beneficial for learning, but also highly redundant. This makes it possible to compress neural networks without having a drastic effect on performance. We introduce targeted dropout, a strategy for post hoc pruning of neural network weights and units that builds the pruning mechanism directly into learning. At each weight update, targeted dropout selects a candidate set for pruning using a simple selection criterion, and then stochastically prunes the network via dropout applied to this set. The resulting network learns to be explicitly robust to pruning, comparing favourably to more complicated regularization schemes while at the same time being extremely simple to implement, and easy to tune.

Aidan N. Gomez, Ivan Zhang, Kevin Swersky, Yarin Gal, Geoffrey E. Hinton

**Workshop on Compact Deep Neural Networks with industrial applications, NeurIPS 2018**[Paper] [BibTex]

**On the Importance of Strong Baselines in Bayesian Deep Learning**

Like all sub-fields of machine learning, Bayesian Deep Learning is driven by empirical validation of its theoretical proposals. Given the many aspects of an experiment, it is always possible that minor or even major experimental flaws can slip by both authors and reviewers. One of the most popular experiments used to evaluate approximate inference techniques is the regression experiment on UCI datasets. However, in this experiment, models which have been trained to convergence have often been compared with baselines trained only for a fixed number of iterations. What we find is that if we take a well-established baseline and evaluate it under the same experimental settings, it shows significant improvements in performance. In fact, it outperforms or performs competitively with numerous to several methods that when they were introduced claimed to be superior to the very same baseline method. Hence, by exposing this flaw in experimental procedure, we highlight the importance of using identical experimental setups to evaluate, compare and benchmark methods in Bayesian Deep Learning.

Jishnu Mukhoti, Pontus Stenetorp, Yarin Gal

**Workshop on Bayesian Deep Learning, NeurIPS 2018**[Paper] [arXiv] [BibTex]

**Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Control**

Self-driving has benefited from significant performance improvements with the rise of deep learning, with millions of miles having been driven with no human intervention. Despite this, crashes and erroneous behaviours still occur, in part due to the complexity of verifying the correctness of DNNs and a lack of safety guarantees. In this paper, we demonstrate how quantitative measures of uncertainty can be extracted in real-time, and their quality evaluated in end-to-end controllers for self-driving cars. We propose evaluation techniques for the uncertainty on two separate architectures which use the uncertainty to predict crashes up to five seconds in advance. We find that mutual information, a measure of uncertainty in classification networks, is a promising indicator of forthcoming crashes.

Rhiannon Michelmore, Marta Kwiatkowska, Yarin Gal

*In submission*

[arXiv] [BibTex]

**Evaluating Bayesian Deep Learning Methods for Semantic Segmentation**

Deep learning has been revolutionary for computer vision and semantic segmentation in particular, with Bayesian Deep Learning (BDL) used to obtain uncertainty maps from deep models when predicting semantic classes. This information is critical when using semantic segmentation for autonomous driving for example. Standard semantic segmentation systems have well-established evaluation metrics. However, with BDL's rising popularity in computer vision we require new metrics to evaluate whether a BDL method produces better uncertainty estimates than another method. In this work we propose three such metrics to evaluate BDL models designed specifically for the task of semantic segmentation. We modify DeepLab-v3+, one of the state-of-the-art deep neural networks, and create its Bayesian counterpart using MC dropout and Concrete dropout as inference techniques. We then compare and test these two inference techniques on the well-known Cityscapes dataset using our suggested metrics. Our results provide new benchmarks for researchers to compare and evaluate their improved uncertainty quantification in pursuit of safer semantic segmentation.

Jishnu Mukhoti, Yarin Gal

*arXiv*

[arXiv] [BibTex]

**Using Bayesian Optimization to Find Asteroids' Pole Directions**

Near-Earth asteroids (NEAs) are being discovered much faster than their shapes and other physical properties can be characterized in detail. One of the best ways to spatially resolve NEAs from the ground is with planetary radar observations. Radar echoes can be decoded in round-trip travel time and frequency to produce two-dimensional delay-Doppler images of the asteroid. Given a series of such images acquired over the course of the asteroid's rotation, one can search for the shape and other physical properties that best match the observations. However, reconstructing asteroid shapes from radar data is, like many inverse problems, a computationally intensive task. Shape modeling also requires extensive human oversight to ensure that the fitting process is finding physically reasonable results. In this paper we use Bayesian optimisation for this difficult task.

Marshall, Sean; Cobb, Adam; Raïssi, Chedy; Gal, Yarin; Rozek, Agata; Busch, Michael W.; Young, Grace; McGlasson, Riley

**American Astronomical Society (AAS), 2018**[Citation] [BibTex]

**Sufficient Conditions for Idealised Models to Have No Adversarial Examples: a Theoretical and Empirical Study with Bayesian Neural Networks**

We prove, under two sufficient conditions, that idealised models can have no adversarial examples. We discuss which idealised models satisfy our conditions, and show that idealised Bayesian neural networks (BNNs) satisfy these. We continue by studying near-idealised BNNs using HMC inference, demonstrating the theoretical ideas in practice. We experiment with HMC on synthetic data derived from MNIST for which we know the ground-truth image density, showing that near-perfect epistemic uncertainty correlates to density under image manifold, and that adversarial images lie off the manifold in our setting. This suggests why MC dropout, which can be seen as performing approximate inference, has been observed to be an effective defence against adversarial examples in practice; We highlight failure-cases of non-idealised BNNs relying on dropout, suggesting a new attack for dropout models and a new defence as well. Lastly, we demonstrate the defence on a cats-vs-dogs image classification task with a VGG13 variant.

Yarin Gal, Lewis Smith

*arXiv, 2018*

[arXiv] [BibTex]

**BRUNO: A Deep Recurrent Model for Exchangeable Data**

We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over observations is invariant under permutation: this property lies at the heart of Bayesian inference. The model does not require variational approximations to train, and new samples can be generated conditional on previous samples, with cost linear in the size of the conditioning set. The advantages of our architecture are demonstrated on learning tasks that require generalisation from short observed sequences while modelling sequence variability, such as conditional image generation, few-shot learning, and anomaly detection.

Iryna Korshunova, Jonas Degrave, Ferenc Huszár, Yarin Gal, Arthur Gretton, Joni Dambre

*arXiv, 2018*

[arXiv] [BibTex]

**NIPS, 2018**[Paper] [BibTex]

**Differentially private continual learning**

Catastrophic forgetting can be a significant problem for institutions that must delete historic data for privacy reasons. For example, hospitals might not be able to retain patient data permanently. But neural networks trained on recent data alone will tend to forget lessons learned on old data. We present a differentially private continual learning framework based on variational inference. We estimate the likelihood of past data given the current model using differentially private generative models of old datasets. The differentially private training has no detrimental impact on our architecture's continual learning performance, and still outperforms the current state-of-the-art non-private continual learning.

Sebastian Farquhar, Yarin Gal

**Privacy in Machine Learning and Artificial Intelligence workshop, ICML, 2018**[Paper] [BibTex]

**Loss-Calibrated Approximate Inference in Bayesian Neural Networks**

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application, and therefore cannot guarantee optimal predictions for a given task. To make more suitable task-specific approximations, we introduce a new loss-calibrated evidence lower bound for Bayesian neural networks in the context of supervised learning, informed by Bayesian decision theory. By introducing a lower bound that depends on a utility function, we ensure that our approximation achieves higher utility than traditional methods for applications that have asymmetric utility functions. Furthermore, in using dropout inference, we highlight that our new objective is identical to that of standard dropout neural networks, with an additional utility-dependent penalty term. We demonstrate our new loss-calibrated model with an illustrative medical example and a restricted model capacity experiment, and highlight failure modes of the comparable weighted cross entropy approach. Lastly, we demonstrate the scalability of our method to real world applications with per-pixel semantic segmentation on an autonomous driving data set.

Adam D. Cobb, Stephen J. Roberts, Yarin Gal

**Theory of deep learning workshop, ICML, 2018**[arXiv] [Code] [BibTex]

**Towards Robust Evaluations of Continual Learning**

Continual learning experiments used in current deep learning papers do not faithfully assess fundamental challenges of learning continually, masking weak-points of the suggested approaches instead. We study gaps in such existing evaluations, proposing essential experimental evaluations that are more representative of continual learning's challenges, and suggest a re-prioritization of research efforts in the field. We show that current approaches fail with our new evaluations and, to analyse these failures, we propose a variational loss which unifies many existing solutions to continual learning under a Bayesian framing, as either 'prior-focused' or 'likelihood-focused'. We show that while prior-focused approaches such as EWC and VCL perform well on existing evaluations, they perform dramatically worse when compared to likelihood-focused approaches on other simple tasks.

Sebastian Farquhar, Yarin Gal

**Lifelong Learning: A Reinforcement Learning Approach workshop, ICML, 2018**[arXiv] [BibTex]

**Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam**

Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to maximum-likelihood methods. In this paper, we propose new natural-gradient algorithms to reduce such efforts for Gaussian mean-field VI. Our algorithms can be implemented within the Adam optimizer by perturbing the network weights during gradient evaluations, and uncertainty estimates can be cheaply obtained by using the vector that adapts the learning rate. This requires lower memory, computation, and implementation effort than existing VI methods, while obtaining uncertainty estimates of comparable quality. Our empirical results confirm this and further suggest that the weight-perturbation in our algorithm could be useful for exploration in reinforcement learning and stochastic optimization.

Mohammad Emtiyaz Khan, Didrik Nielsen, Voot Tangkaratt, Wu Lin, Yarin Gal, Akash Srivastava

**ICML, 2018**[Paper] [arXiv] [BibTex]

**Understanding Measures of Uncertainty for Adversarial Example Detection**

Measuring uncertainty is a promising technique for detecting adversarial examples, crafted inputs on which the model predicts an incorrect class with high confidence. But many measures of uncertainty exist, including predictive en- tropy and mutual information, each capturing different types of uncertainty. We study these measures, and shed light on why mutual information seems to be effective at the task of adversarial example detection. We highlight failure modes for MC dropout, a widely used approach for estimating uncertainty in deep models. This leads to an improved understanding of the drawbacks of current methods, and a proposal to improve the quality of uncertainty estimates using probabilistic model ensembles. We give illustrative experiments using MNIST to demonstrate the intuition underlying the different measures of uncertainty, as well as experiments on a real world Kaggle dogs vs cats classification dataset.

Lewis Smith, Yarin Gal

**UAI, 2018**[Paper] [arXiv] [BibTex]

**Using Pre-trained Full-Precision Models to Speed Up Training Binary Networks For Mobile Devices**

Binary Neural Networks (BNNs) are well-suited for deploying Deep Neural Networks (DNNs) to small embedded devices but state-of-the-art BNNs need to be trained from scratch. We show how weights from a trained full-precision model can be used to speed-up training binary networks. We show that for CIFAR-10, accuracies within 1% of the full-precision model can be achieved in just 5 epochs.

Milad Alizadeh, Nicholas D. Lane, Yarin Gal

**16th ACM International Conference on Mobile Systems (MobiSys), 2018**[Abstract] [BibTex]

**Automating Asteroid Shape Modeling From Radar Images**

Characterizing the shapes and spin states of near-Earth asteroids is essential both for trajectory predictions to rule out potential future Earth impacts and for planning spacecraft missions. But reconstructing objects’ shapes and spins from delay-Doppler data is a computationally intensive inversion problem. We implement a Bayesian optimization routine that uses SHAPE to autonomously search the space of spin-state parameters, yielding spin state constraints within a factor of 3 less computer runtime and minimal human supervision. These routines are now being incorporated into radar data processing pipelines at Arecibo.

Michael W. Busch, Agata Rozek, Sean Marshall, Grace Young, Adam Cobb, Chedy Raissi, Yarin Gal, Lance Benner, Shantanu Naidu, Marina Brozovic, Patrick Taylor

**COSPAR (Committee on Space Research) Assembly, 2018**[Program] [Blog Post (Adam Cobb)] [BibTex]

**Vprop: Variational Inference using RMSprop**

Many computationally-efficient methods for Bayesian deep learning rely on continuous optimization algorithms, but the implementation of these methods requires significant changes to existing code-bases. In this paper, we propose Vprop, a method for variational inference that can be implemented with two minor changes to the off-the-shelf RMSprop optimizer. Vprop also reduces the memory requirements of Black-Box Variational Inference by half. We derive Vprop using the conjugate-computation variational inference method, and establish its connections to Newton’s method, natural-gradient methods, and extended Kalman filters. Overall, this paper presents Vprop as a principled, computationally-efficient, and easy-to-implement method for Bayesian deep learning.

Mohammad Emtiyaz Khan, Zuozhu Liu, Voot Tangkaratt, Yarin Gal

**Bayesian Deep Learning workshop, NIPS, 2017**[Paper] [arXiv] [BibTex]