OATML

Weight space symmetries in neural network architectures, such as permutation symmetries in MLPs, give rise to Bayesian neural network (BNN) posteriors with many equivalent modes. This multimodality poses a challenge for variational inference (VI) techniques, which typically rely on approximating the posterior with a unimodal distribution. In this work, we investigate the impact of weight space permutation symmetries on VI. We demonstrate, both theoretically and empirically, that these symmetries lead to biases in the approximate posterior, which degrade predictive performance and posterior fit if not explicitly accounted for. To mitigate this behavior, we leverage the symmetric structure of the posterior and devise a symmetrization mechanism for constructing permutation invariant variational posteriors. We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective with a modified KL regular... [full abstract]

Fully supervised models are predominant in Bayesian active learning. We argue that their neglect of the information present in unlabelled data harms not just predictive performance but also decisions about what data to acquire. Our proposed solution is a simple framework for semi-supervised Bayesian active learning. We find it produces better-performing models than either conventional Bayesian active learning or semi-supervised learning with randomly acquired data. It is also easier to scale up than the conventional approach. As well as supporting a shift towards semi-supervised models, our findings highlight the importance of studying models and acquisition methods in conjunction.

Accelerating the discovery of novel and more effective therapeutics is a major pharmaceutical problem in which deep learning plays an increasingly important role. However, drug discovery tasks are often characterized by a scarcity of labeled data and significant covariate shift—settings that are challenging for standard deep learning methods. In this paper, we address this challenge by developing a probabilistic model that is able to encode prior knowledge about the data-generating process into a prior distribution over functions, allowing researchers to explicitly specify relevant information about the modeled domain. We evaluate this method on a novel, high-quality antimalarial dataset that facilitates the robust comparison of models in an extrapolative regime and demonstrate that integrating explicit prior knowledge of drug-like chemical space into the modeling process substantially improves both the predictive accuracy and the uncertainty estimates of deep learning algorithm... [full abstract]

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting — a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a single target-state pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-value pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of multi-target-state interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-targe... [full abstract]

Information-theoretic approaches to active learning have traditionally focused on maximising the information gathered about the model parameters, most commonly by optimising the BALD score. We highlight that this can be suboptimal from the perspective of predictive performance. For example, BALD lacks a notion of an input distribution and so is prone to prioritise data of limited relevance. To address this we propose the expected predictive information gain (EPIG), an acquisition function that measures information gain in the space of predictions rather than parameters. We find that using EPIG leads to stronger predictive performance compared with BALD across a range of datasets and models, and thus provides an appealing drop-in replacement.

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a prior distribution over the network parameters, infer an approximate posterior distribution, and use it to make stochastic predictions. However, explicit inference over neural network parameters makes it difficult to incorporate meaningful prior information about the data-generating process into the model. In this paper, we pursue an alternative approach. Recognizing that the primary object of interest in most settings is the distribution over functions induced by the posterior distribution over neural network parameters, we frame Bayesian inference in neural networks explicitly as inferring a posterior distribution over functions and propose a scalable function-space variational inference method that allows incorporating prior information and re... [full abstract]

The development and deployment of machine learning systems can be executed easily with modern tools, but the process is typically rushed and means-to-an-end. Lack of diligence can lead to technical debt, scope creep and misaligned objectives, model misuse and failures, and expensive consequences. Engineering systems, on the other hand, follow well-defined processes and testing standards to streamline development for high-quality, reliable results. The extreme is spacecraft systems, with mission critical measures and robustness throughout the process. Drawing on experience in both spacecraft engineering and machine learning (research through product across domain areas), we’ve developed a proven systems engineering approach for machine learning and artificial intelligence: the Machine Learning Technology Readiness Levels framework defines a principled process to ensure robust, reliable, and responsible systems while being streamlined for machine learning workflows, including key ... [full abstract]

Being able to quantify uncertainty when comparing a theoretical or computational model to observations is critical to conducting a sound scientific investigation. With the rise of data-driven modelling, understanding various sources of uncertainty and developing methods to estimate them has gained renewed attention. Yarin Gal and four other experts discuss uncertainty quantification in machine-learned models with an emphasis on issues relevant to physics problems.

A recent trend in artificial intelligence is the use of pretrained models for language and vision tasks, which have achieved extraordinary performance but also puzzling failures. Probing these models’ abilities in diverse ways is therefore critical to the field. In this paper, we explore the reliability of models, where we define a reliable model as one that not only achieves strong predictive performance but also performs well consistently over many decision-making tasks involving uncertainty (e.g., selective prediction, open set recognition), robust generalization (e.g., accuracy and proper scoring rules such as log-likelihood on in- and out-of-distribution datasets), and adaptation (e.g., active learning, few-shot uncertainty). We devise 10 types of tasks over 40 datasets in order to evaluate different aspects of reliability on both vision and language domains. To improve reliability, we developed ViT-Plex and T5-Plex, pretrained large model extensions for vision and language... [full abstract]

Sequential Bayesian inference over predictive functions is a natural framework for continual learning from streams of data. However, applying it to neural networks has proved challenging in practice. Addressing the drawbacks of existing techniques, we propose an optimization objective derived by formulating continual learning as sequential function-space variational inference. In contrast to existing methods that regularize neural network parameters directly, this objective allows parameters to vary widely during training, enabling better adaptation to new tasks. Compared to objectives that directly regularize neural network predictions, the proposed objective allows for more flexible variational distributions and more effective regularization. We demonstrate that, across a range of task sequences, neural networks trained via sequential function-space variational inference achieve better predictive accuracy than networks trained with related methods while depending less on maint... [full abstract]

Causal discovery from observational and interventional data is challenging due to limited data and non-identifiability: factors that introduce uncertainty in estimating the underlying structural causal model (SCM). Selecting experiments (interventions) based on the uncertainty arising from both factors can expedite the identification of the SCM. Existing methods in experimental design for causal discovery from limited data either rely on linear assumptions for the SCM or select only the intervention target. This work incorporates recent advances in Bayesian causal discovery into the Bayesian optimal experimental design framework, allowing for active causal discovery of large, nonlinear SCMs while selecting both the interventional target and the value. We demonstrate the performance of the proposed method on synthetic graphs (Erdos-Rènyi, Scale Free) for both linear and nonlinear SCMs as well as on the in-silico single-cell gene regulatory network dataset, DREAM.

We provide a stochastic strategy for adapting well-known acquisition functions to allow batch active learning. In deep active learning, labels are often acquired in batches for efficiency. However, many acquisition functions are designed for single-sample acquisition and fail when naively used to construct batches. In contrast, state-of-the-art batch acquisition functions are costly to compute. We show how to extend single-sample acquisition functions to the batch setting. Instead of acquiring the top-K points from the pool set, we account for the fact that acquisition scores are expected to change as new points are acquired. This motivates simple stochastic acquisition strategies using score-based or rank-based distributions. Our strategies outperform the standard top-K acquisition with virtually no computational overhead and can be used as a drop-in replacement. In fact, they are even competitive with much more expensive methods despite their linear computational complexity. We c... [full abstract]

Principled Bayesian deep learning (BDL) does not live up to its potential when we only focus on marginal predictive distributions (marginal predictives). Recent works have highlighted the importance of joint predictives for (Bayesian) sequential decision making from a theoretical and synthetic perspective. We provide additional practical arguments grounded in realworld applications for focusing on joint predictives: we discuss online Bayesian inference, which would allow us to make predictions while taking into account additional data without retraining, and we propose new challenging evaluation settings using active learning and active sampling. These settings are motivated by an examination of marginal and joint predictives, their respective cross-entropies, and their place in offline and online learning. They are more realistic than previously suggested ones, building on work by Wen et al. (2021) and Osband et al. (2022), and focus on evaluating the performance of approximate... [full abstract]

Inducing point Gaussian process approximations are often considered a gold standard in uncertainty estimation since they retain many of the properties of the exact GP and scale to large datasets. A major drawback is that they have difficulty scaling to high dimensional inputs. Deep Kernel Learning (DKL) promises a solution: a deep feature extractor transforms the inputs over which an inducing point Gaussian process is defined. However, DKL has been shown to provide unreliable uncertainty estimates in practice. We study why, and show that with no constraints, the DKL objective pushes “far-away” data points to be mapped to the same features as those of training-set points. With this insight we propose to constrain DKL’s feature extractor to approximately preserve distances through a bi-Lipschitz constraint, resulting in a feature space favorable to DKL. We obtain a model, DUE, which demonstrates uncertainty quality outperforming previous DKL and other single forward pass uncertain... [full abstract]

Uncertainty representation is crucial to the safe and reliable deployment of deep learning. Bayesian methods provide a natural mechanism to represent epistemic uncertainty, leading to improved generalization and calibrated predictive distributions. Understanding the fidelity of approximate inference has extraordinary value beyond the standard approach of measuring generalization on a particular task: if approximate inference is working correctly, then we can expect more reliable and accurate deployment across any number of real-world settings. In this competition, we evaluate the fidelity of approximate Bayesian inference procedures in deep learning, using as a reference Hamiltonian Monte Carlo (HMC) samples obtained by parallelizing computations over hundreds of tensor processing unit (TPU) devices. We consider a variety of tasks, including image recognition, regression, covariate shift, and medical applications. All data are publicly available, and we release several baselines... [full abstract]

Bayesian deep learning seeks to equip deep neural networks with the ability to precisely quantify their predictive uncertainty, and has promised to make deep learning more reliable for safety-critical real-world applications. Yet, existing Bayesian deep learning methods fall short of this promise; new methods continue to be evaluated on unrealistic test beds that do not reflect the complexities of downstream real-world tasks that would benefit most from reliable uncertainty quantification. We propose a set of real-world tasks that accurately reflect such complexities and are designed to assess the reliability of predictive models in safety-critical scenarios. Specifically, we curate two publicly available datasets of high-resolution human retina images exhibiting varying degrees of diabetic retinopathy, a medical condition that can lead to blindness, and use them to design a suite of automated diagnosis tasks that require reliable predictive uncertainty quantification. We use th... [full abstract]

High-quality estimates of uncertainty and robustness are crucial for numerous real-world applications, especially for deep learning which underlies many deployed ML systems. The ability to compare techniques for improving these estimates is therefore very important for research and practice alike. Yet, competitive comparisons of methods are often lacking due to a range of reasons, including: compute availability for extensive tuning, incorporation of sufficiently many baselines, and concrete documentation for reproducibility. In this paper we introduce Uncertainty Baselines: high-quality implementations of standard and state-of-the-art deep learning methods on a variety of tasks. As of this writing, the collection spans 19 methods across 9 tasks, each with at least 5 metrics. Each baseline is a self-contained experiment pipeline with easily reusable and extendable components. Our goal is to provide immediate starting points for experimentation with new methods or applications. A... [full abstract]

Aerosol-cloud interactions include a myriad of effects that all begin when aerosol enters a cloud and acts as cloud condensation nuclei (CCN). An increase in CCN results in a decrease in the mean cloud droplet size (r$_{e}$). The smaller droplet size leads to brighter, more expansive, and longer lasting clouds that reflect more incoming sunlight, thus cooling the earth. Globally, aerosol-cloud interactions cool the Earth, however the strength of the effect is heterogeneous over different meteorological regimes. Understanding how aerosol-cloud interactions evolve as a function of the local environment can help us better understand sources of error in our Earth system models, which currently fail to reproduce the observed relationships. In this work we use recent non-linear, causal machine learning methods to study the heterogeneous effects of aerosols on cloud droplet radius.

We extend Deep Deterministic Uncertainty (DDU), a method for uncertainty estimation using feature space densities, to semantic segmentation. DDU enables quantifying and disentangling epistemic and aleatoric uncertainty in a single forward pass through the model. We study the similarity of feature representations of pixels at different locations for the same class and conclude that it is feasible to apply DDU location independently, which leads to a significant reduction in memory consumption compared to pixel dependent DDU. Using the DeepLab-v3+ architecture on Pascal VOC 2012, we show that DDU improves upon MC Dropout and Deep Ensembles while being significantly faster to compute.

Estimating personalized treatment effects from high-dimensional observational data is essential in situations where experimental designs are infeasible, unethical or expensive. Existing approaches rely on fitting deep models on outcomes observed for treated and control populations, but when measuring the outcome for an individual is costly (e.g. biopsy) a sample efficient strategy for acquiring outcomes is required. Deep Bayesian active learning provides a framework for efficient data acquisition by selecting points with high uncertainty. However, naive application of existing methods selects training data that is biased toward regions where the treatment effect cannot be identified because there is non-overlapping support between the treated and control populations. To maximize sample efficiency for learning personalized treatment effects, we introduce new acquisition functions grounded in information theory that bias data acquisition towards regions where overlap is satisfied,... [full abstract]

There has been significant research done on developing methods for improving robustness to distributional shift and uncertainty estimation. In contrast, only limited work has examined developing standard datasets and benchmarks for assessing these approaches. Additionally, most work on uncertainty estimation and robustness has developed new techniques based on small-scale regression or image classification tasks. However, many tasks of practical interest have different modalities, such as tabular data, audio, text, or sensor data, which offer significant challenges involving regression and discrete or continuous structured prediction. Thus, given the current state of the field, a standardized large-scale dataset of tasks across a range of modalities affected by distributional shifts is necessary. This will enable researchers to meaningfully evaluate the plethora of recently developed uncertainty quantification methods, as well as assessment criteria and state-of-the-art baselin... [full abstract]

Optimization in the latent space of variational autoencoders is a promising approach to generate high-dimensional discrete objects that maximize an expensive black-box property (e.g., drug-likeness in molecular generation, function approximation with arithmetic expressions). However, existing methods lack robustness as they may decide to explore areas of the latent space for which no data was available during training and where the decoder can be unreliable, leading to the generation of unrealistic or invalid objects. We propose to leverage the epistemic uncertainty of the decoder to guide the optimization process. This is not trivial though, as a naive estimation of uncertainty in the high-dimensional and structured settings we consider would result in high estimator variance. To solve this problem, we introduce an importance sampling-based estimator that provides more robust estimates of epistemic uncertainty. Our uncertainty-guided optimization approach does not require modif... [full abstract]

While Deep Ensembles are the state-of-the art for uncertainty prediction, standard softmax neural nets suffer from feature collapse and cannot disentangle aleatoric and epistemic uncertainty. We show that a single softmax neural net with minimal changes can beat epistemic uncertainty predictions of Deep Ensembles and other complex single-forward-pass uncertainty approaches (DUQ and SNGP) while also disentangling uncertainties. Our Deep Deterministic Uncertainty (DDU) is based on three insights: i) predictive entropy confounds aleatoric and epistemic uncertainty, and softmax entropy is inconsistent for OoD points; ii) with appropriate inductive biases, i.e. residual connections and spectral normalization, feature-space density reliably captures epistemic uncertainty; and, iii) density estimation and classification objectives might have different optima. Thus, DDU disentangles aleatoric uncertainty using softmax entropy and epistemic uncertainty using a separate featur... [full abstract]

Entropy of a predictive distribution averaged over an ensemble or several posterior weight samples is often used as a metric for Out-of-Distribution (OoD) detection. However, we show that predictive entropy is inappropriate for this task because it mistakes ambiguous in-distribution samples as OoD. This issue remains hidden on curated datasets commonly used for benchmarking. We introduce a new dataset, Dirty-MNIST, with a long tail of ambiguous samples, which exemplifies this problem. Additionally, we look at the entropy of single, deterministic, softmax models and show that it is unreliable exactly for OoD samples. In summary, we caution against using predictive or softmax entropy for OoD detection in practice and introduce several methods to evaluate the quantitative difference between several uncertainty metrics.

ResNets constrained to be bi-Lipschitz, that is, approximately distance preserving, have been a crucial component of recently proposed techniques for deterministic uncertainty quantification in neural models. We show that theoretical justifications for recent regularisation schemes trying to enforce such a constraint suffer from a crucial flaw – the theoretical link between the regularisation scheme used and bi-Lipschitzness is only valid under conditions which do not hold in practice, rendering existing theory of limited use, despite the strong empirical performance of these models. We provide a theoretical explanation for the effectiveness of these regularisation schemes using a frequency analysis perspective, showing that under mild conditions these schemes will enforce a lower Lipschitz bound on the low-frequency projection of images. We then provide empirical evidence supporting our theoretical claims, and perform further experiments which demonstrate that our broader concl... [full abstract]

We show that the gradient estimates used in training Deep Gaussian Processes (DGPs) with importance-weighted variational inference are susceptible to signal-to-noise ratio (SNR) issues. Specifically, we show both theoretically and empirically that the SNR of the gradient estimates for the latent variable’s variational parameters decreases as the number of importance samples increases. As a result, these gradient estimates degrade to pure noise if the number of importance samples is too large. To address this pathology, we show how doubly-reparameterized gradient estimators, originally proposed for training variational autoencoders, can be adapted to the DGP setting and that the resultant estimators completely remedy the SNR issue, thereby providing more reliable training. Finally, we demonstrate that our fix can lead to improvements in the predictive performance of the model’s predictive posterior.

We introduce active testing: a new framework for sample-efficient model evaluation. While approaches like active learning reduce the number of labels needed for model training, existing literature largely ignores the cost of labeling test data, typically unrealistically assuming large test sets for model evaluation. This creates a disconnect to real applications where test labels are important and just as expensive, e.g. for optimizing hyperparameters. Active testing addresses this by carefully selecting the test points to label, ensuring model evaluation is sample-efficient. To this end, we derive theoretically-grounded and intuitive acquisition strategies that are specifically tailored to the goals of active testing, noting these are distinct to those of active learning. Actively selecting labels introduces a bias; we show how to remove that bias while reducing the variance of the estimator at the same time. Active testing is easy to implement, effective, and can be applied to... [full abstract]

We study the problem of learning conditional average treatment effects (CATE) from high-dimensional, observational data with unobserved confounders. Unobserved confounders introduce ignorance – a level of unidentifiability – about an individual’s response to treatment by inducing bias in CATE estimates. We present a new parametric interval estimator suited for high-dimensional data, that estimates a range of possible CATE values when given a predefined bound on the level of hidden confounding. Further, previous interval estimators do not account for ignorance about the CATE stemming from samples that may be underrepresented in the original study, or samples that violate the overlap assumption. Our novel interval estimator also incorporates model uncertainty so that practitioners can be made aware of out-of-distribution data. We prove that our estimator converges to tight bounds on CATE when there may be unobserved confounding, and assess it using semi-synthetic, high-dimensional... [full abstract]

We introduce Deep Adaptive Design (DAD), a general method for amortizing the cost of performing sequential adaptive experiments using the framework of Bayesian optimal experimental design (BOED). Traditional sequential BOED approaches require substantial computational time at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate tha... [full abstract]

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic conditioning. However, in many real-life scenarios, the observations are given as marginal distributions, summary statistics, or samplers. Conventional probabilistic programming systems lack adequate means for modeling and inference in such scenarios. We propose a generalization of deterministic conditioning to stochastic conditioning, that is, conditioning on the marginal distribution of a variable taking a particular form. To this end, we first define the formal notion of stochastic conditioning and discuss its key properties. We then show how to perform inference in the presence of stochastic conditioning. We demonstrate potential usage of stochastic conditioning on several case studies which involve various kinds of stochastic conditioning and are d... [full abstract]

Research in machine learning for autonomous driving (AD) is a constantly evolving field as researchers strive to build a Level 5 autonomous driving system. However, current benchmarks for such learning algorithms do not satisfactorily allow researchers to evaluate and compare performance across safety-critical metrics such as generalizability, out-of-distribution performance, etc. Reasons for this include the expensive nature of data collection from the real-world for autonomous driving and the limitations of software tools currently available for autonomous driving simulators. We develop a pipeline that allows for automatic generation of new town maps for simulator environments from OpenStreetMap [Haklay and Weber, 2008]. We demonstrate that our pipeline is capable of generating towns that, when perceived via LiDAR , share similar footprint to real-world gathered datasets like NuScenes [Caesar et al., 2020]. Additionally, we learn a realistic noise augmentation via Conditional ... [full abstract]

We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model’s training speed can be used to estimate its marginal likelihood. Second, that this measure, under certain conditions, predicts the relative weighting of models in linear model combinations trained to minimize a regression loss. We verify our results in model selection tasks for linear models and for the infinite-width limit of deep neural networks. We further provide encouraging empirical evidence that the intuition developed in these settings also holds for deep neural networks trained with stochastic gradient descent. Our results suggest a promising new direction towards explaining why neural networks trained with stochastic gradient descent are biased towards functions that generalize well.

We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distributions in function-space to those induced by shallower networks with complex weight posteriors. We validate our theoretical contributions empirically, both through examination of the weight posterior using Hamiltonian Monte Carlo in small models and by comparing diagonal- to structured-covariance in large settings. Since complex variational posteriors are often expensive and cumbersome to implement, our results suggest that using mean-field variational inference in a deeper model is both a practical and theoretically justified alternative to structured approximations.

While deep learning algorithms can excel at predicting outcomes, they often act as black-boxes rendering them uninterpretable for healthcare practitioners. Counterfactual explanations (CEs) are a practical tool for demonstrating why machine learning models make particular decisions. We introduce a novel algorithm that leverages uncertainty to generate trustworthy counterfactual explanations for white-box models. Our proposed method can generate more interpretable CEs than the current benchmark (Van Looveren and Klaise, 2019) for breast cancer diagnosis. Further, our approach provides confidence levels for both the diagnosis as well as the explanation.

Recommending the best course of action for an individual is a major application of individual-level causal effect estimation. This application is often needed in safety-critical domains such as healthcare, where estimating and communicating uncertainty to decision-makers is crucial. We introduce a practical approach for integrating uncertainty estimation into a class of state-of-the-art neural network methods used for individual-level causal estimates. We show that our methods enable us to deal gracefully with situations of “no-overlap”, common in high-dimensional data, where standard applications of causal effect approaches fail. Further, our methods allow us to handle covariate shift, where test distribution differs to train distribution, common when systems are deployed in practice. We show that when such a covariate shift occurs, correctly modeling uncertainty can keep us from giving overconfident and potentially harmful recommendations. We demonstrate our methodology with a... [full abstract]

The ability to quantify the uncertainty in the prediction of a Bayesian deep learning model has significant practical implications—from more robust machine-learning based systems to more effective expert-in-the loop processes. While several general measures of model uncertainty exist, they are often intractable in practice when dealing with high dimensional data such as long sequences. Instead, researchers often resort to ad hoc approaches or to introducing independence assumptions to make computation tractable. We introduce a principled approach to estimate uncertainty in high dimensions that circumvents these challenges, and demonstrate its benefits in de novo molecular design.

The Information Bottleneck principle offers both a mechanism to explain how deep neural networks train and generalize, as well as a regularized objective with which to train models. However, multiple competing objectives are proposed in the literature, and the information-theoretic quantities used in these objectives are difficult to compute for large deep neural networks, which in turn limits their use as a training objective. In this work, we review these quantities and compare and unify previously proposed objectives, which allows us to develop surrogate objectives more friendly to optimization without relying on cumbersome tools such as density estimation. We find that these surrogate objectives allow us to apply the information bottleneck to modern neural network architectures. We demonstrate our insights on MNIST, CIFAR-10 and Imagenette with modern DNN architectures (ResNets).

The Information Bottleneck (IB) principle characterizes learning and generalization in deep neural networks in terms of the change in two information theoretic quantities and leads to a regularized objective function for training neural networks. These quantities are difficult to compute directly for deep neural networks. We show that it is possible to backpropagate through a simple entropy estimator to obtain an IB training method that works for modern neural network architectures. We evaluate our approach empirically on the CIFAR-10 dataset, showing that IB objectives can yield competitive performance on this dataset with a conceptually simple approach while also performing well against adversarial attacks out-of-the-box.

We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. Our approach, deterministic uncertainty quantification (DUQ), builds upon ideas of RBF networks. We scale training in these with a novel loss function and centroid updating scheme and match the accuracy of softmax models. By enforcing detectability of changes in the input using a gradient penalty, we are able to reliably detect out of distribution data. Our uncertainty quantification scales well to large datasets, and using a single model, we improve upon or match Deep Ensembles in out of distribution detection on notable difficult dataset pairs such as FashionMNIST vs. MNIST, and CIFAR-10 vs. SVHN.

Inter-domain Gaussian processes (GPs) allow for high flexibility and low computational cost when performing approximate inference in GP models. They are particularly suitable for modeling data exhibiting global structure but are limited to stationary covariance functions and thus fail to model non-stationary data effectively. We propose Inter-domain Deep Gaussian Processes, an extension of inter-domain shallow GPs that combines the advantages of inter-domain and deep Gaussian processes (DGPs), and demonstrate how to leverage existing approximate inference methods to perform simple and scalable approximate inference using inter-domain features in DGPs. We assess the performance of our method on a range of regression tasks and demonstrate that it outperforms inter-domain shallow GPs and conventional DGPs on challenging large-scale real-world datasets exhibiting both global structure as well as a high-degree of non-stationarity.

Out-of-training-distribution (OOD) scenarios are a common challenge of learning agents at deployment, typically leading to arbitrary deductions and poorly-informed decisions. In principle, detection of and adaptation to OOD scenes can mitigate their adverse effects. In this paper, we highlight the limitations of current approaches to novel driving scenes and propose an epistemic uncertainty-aware planning method, called robust imitative planning (RIP). Our method can detect and recover from some distribution shifts, reducing the overconfident and catastrophic extrapolations in OOD scenes. If the model’s uncertainty is too great to suggest a safe course of action, the model can instead query the expert driver for feedback, enabling sample-efficient online adaptation, a variant of our method we term adaptive robust imitative planning (AdaRIP). Our methods outperform current state-of-the-art approaches in the nuScenes prediction challenge, but since no be... [full abstract]

In this paper, we develop a metric designed to assess and rank uncertainty measures for the task of brain tumour sub-tissue segmentation in the BraTS 2019 sub-challenge on uncertainty quantification. The metric is designed to: (1) reward uncertainty measures where high confidence is assigned to correct assertions, and where incorrect assertions are assigned low confidence and (2) penalize measures that have higher percentages of under-confident correct assertions. Here, the workings of the components of the metric are explored based on a number of popular uncertainty measures evaluated on the BraTS 2019 dataset.

Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the controller behaviour that properly take account of the uncertainty within the model as well as sensor noise. Bayesian neural networks, which assume a prior over the weights, have been shown capable of producing such uncertainty measures, but properties surrounding their safety have not yet been quantified for use in autonomous driving scenarios. In this paper, we develop a framework based on a state-of-the-art simulator for evaluating end-to-end Bayesian controllers. In addition to computing pointwise uncertainty measures that can be computed in real time and with statistical guarantees, we also provide a method for estimating the probability that, given a scenario, the controller keeps the car safe within a finite horizon. We experimentally ev... [full abstract]

We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive. We argue mathematically that full-covariance approximations only improve the ELBO if they improve the expected log-likelihood. We further show that deeper mean-field networks are able to express predictive distributions approximately equivalent to shallower full-covariance networks. We validate these observations empirically, demonstrating that deeper models decrease the divergence between diagonal- and full-covariance Gaussian fits to the true posterior.

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning methods, like MC dropout or deep ensembles, have discrete support—they assign zero probability to almost all of the weight-space. Unlike these discrete support methods, Radial BNNs’ full support makes them suitable for use as a prior for sequential inference. In addition, they solve the conceptual challenges with the a priori implausibility of weight distributions with discrete support. The Radial BNN is motivated by avoiding a sampling problem in ‘mean-field’ variational inference (MFVI) caused by the so-called ‘soap-bubble’ pathology of multivariate Gaussians. We show that, unlike MFVI, Radial BNNs are robust to hyperparameters and can be efficiently applied to a challenging real-world medical application without needing ad-hoc tweaks and inte... [full abstract]

Trading off exploration and exploitation in an unknown environment is key to maximising expected return during learning. A Bayes-optimal policy, which does so optimally, conditions its actions not only on the environment state but on the agent’s uncertainty about the environment. Computing a Bayes-optimal policy is however intractable for all but the smallest tasks. In this paper, we introduce variational Bayes-Adaptive Deep RL (variBAD), a way to meta-learn to perform approximate inference in an unknown environment, and incorporate task uncertainty directly during action selection. In a grid-world domain, we illustrate how variBAD performs structured online exploration as a function of task uncertainty. We also evaluate variBAD on MuJoCo domains widely used in meta-RL and show that it achieves higher return during training than existing methods.

Black-box adversarial attacks require a large number of attempts before finding successful adversarial examples that are visually indistinguishable from the original input. Current approaches relying on substitute model training, gradient estimation or genetic algorithms often require an excessive number of queries. Therefore, they are not suitable for real-world systems where the maximum query number is limited due to cost. We propose a query-efficient black-box attack which uses Bayesian optimisation in combination with Bayesian model selection to optimise over the adversarial perturbation and the optimal degree of search space dimension reduction. We demonstrate empirically that our method can achieve comparable success rates with 2-5 times fewer queries compared to previous state-of-the-art black-box attacks.

We use epistemic uncertainty to detect out-of-training-distribution sentences in Neural Machine Translation. For this, we develop a measure of uncertainty designed specifically for long sequences of discrete random variables, corresponding to the words in the output sentence. This measure is able to convey epistemic uncertainty akin to the Mutual Information (MI), which is used in the case of single discrete random variables such as in classification. Our new measure of uncertainty solves a major intractability in the naive application of existing approaches on long sentences. We train a Transformer model with dropout on the task of GermanEnglish translation using WMT 13 and Europarl, and show that using dropout uncertainty our measure is able to identify when Dutch source sentences, sentences which use the same word types as German, are given to the model instead of German.

Inverse reinforcement learning has proved its ability to explain state-action trajectories of expert agents by recovering their underlying reward functions in increasingly challenging environments. Recent advances in adversarial learning have allowed extending inverse RL to applications with non-stationary environment dynamics unknown to the agents, arbitrary structures of reward functions and improved handling of the ambiguities inherent to the ill-posed nature of inverse RL. This is particularly relevant in real time applications on stochastic environments involving risk, like volatile financial markets. Moreover, recent work on simulation of complex environments enable learning algorithms to engage with real market data through simulations of its latent space representations, avoiding a costly exploration of the original environment. In this paper, we explore whether adversarial inverse RL algorithms can be adapted and trained within such latent space simulations from real ma... [full abstract]

Learning from expert demonstrations is an attractive framework for sequential decision-making in safety-critical domains such as autonomous driving, where trial and error learning has no safety guarantees during training. However, naïve use of imitation learning can fail by extrapolating incorrectly to unfamiliar situations, resulting in arbitrary model outputs and dangerous outcomes. This is especially true for high capacity parametric models such as deep neural networks, for processing high-dimensional observations from cameras or LIDAR. Instead, we model expert behaviour with a model able to capture uncertainty about previously unseen scenarios, as well as inherent stochasticity in expert demonstrations. We propose a framework for planning under epistemic uncertainty and also provide a practical realisation, called robust imitative planning (RIP), using an ensemble of deep neural density estimators. We demonstrate online robustness to out-of-training distribution scenarios on... [full abstract]

Gradient-based optimization methods have proven successful in learning complex, overparameterized neural networks from non-convex objectives. Yet, the precise theoretical relationship between gradient-based optimization methods, the resulting training dynamics, and generalization in deep neural networks (DNNs) remains unclear. In this work, we investigate the training dynamics of overparameterized DNNs of \emph{finite-width} under natural gradient descent. To do so, we take a function-space view of the training dynamics under natural gradient descent and derive a bound on the discrepancy between the DNN predictive distributions induced by linearized and non-linearized natural gradient descent. Unlike prior work, our bound quantifies the extent to which linearization of the training dynamics of finite-width DNNs affects DNN predictions on arbitrary test points.

Specifying meaningful weight priors for variational inference in Bayesian deep neural network (DNN) is a challenging problem, particularly for scaling to larger models involving high dimensional weight space. We evaluate the recently proposed, MOdel Priors with Empirical Bayes using DNN (MOPED) method for Bayesian DNNs within the Bayesian Deep Learning (BDL) benchmarking framework. MOPED enables scalable VI in large models by providing a way to choose informed prior and approximate posterior distributions for Bayesian neural network weights using Empirical Bayes framework. We benchmark MOPED with mean field variational inference on a real-world diabetic retinopathy diagnosis task and compare with state-of-the-art BDL techniques. We demonstrate MOPED method provides reliable uncertainty estimates while outperforming state-of-the-art methods, offering a new strong baseline for the BDL community to compare on complex real-world tasks involving larger models.

Machine learning techniques have been successfully applied to super-resolution tasks on natural images where visually pleasing results are sufficient. However in many scientific domains this is not adequate and estimations of errors and uncertainties are crucial. To address this issue we propose a Bayesian framework that decomposes uncertainties into epistemic and aleatoric uncertainties. We test the validity of our approach by super-resolving images of the Sun’s magnetic field and by generating maps measuring the range of possible high resolution explanations compatible with a given low resolution magnetogram.

Evaluation of Bayesian deep learning (BDL) methods is challenging. We often seek to evaluate the methods’ robustness and scalability, assessing whether new tools give ‘better’ uncertainty estimates than old ones. These evaluations are paramount for practitioners when choosing BDL tools on-top of which they build their applications. Current popular evaluations of BDL methods, such as the UCI experiments, are lacking: Methods that excel with these experiments often fail when used in application such as medical or automotive, suggesting a pertinent need for new benchmarks in the field. We propose a new BDL benchmark with a diverse set of tasks, inspired by a real-world medical imaging application on diabetic retinopathy diagnosis. Visual inputs (512x512 RGB images of retinas) are considered, where model uncertainty is used for medical pre-screening—i.e. to refer patients to an expert when model diagnosis is uncertain. Methods are then ranked according to metrics derived from expert... [full abstract]

We develop BatchBALD, a tractable approximation to the mutual information between a batch of points and model parameters, which we use as an acquisition function to select multiple informative points jointly for the task of deep Bayesian active learning. BatchBALD is a greedy linear-time 1−1/e-approximate algorithm amenable to dynamic programming and efficient caching. We compare BatchBALD to the commonly used approach for batch data acquisition and find that the current approach acquires similar and redundant points, sometimes performing worse than randomly acquiring data. We finish by showing that, using BatchBALD to consider dependencies within an acquisition batch, we achieve new state of the art performance on standard benchmarks, providing substantial data efficiency improvements in batch acquisition.

Applying probabilistic models to reinforcement learning (RL) enables the application of powerful optimisation tools such as variational inference to RL. However, existing inference frameworks and their algorithms pose significant challenges for learning optimal policies, e.g., the absence of mode capturing behaviour in pseudo-likelihood methods and difficulties learning deterministic policies in maximum entropy RL based approaches. We propose VIREL, a novel, theoretically grounded probabilistic inference framework for RL that utilises a parametrised action-value function to summarise future dynamics of the underlying MDP. This gives VIREL a mode-seeking form of KL divergence, the ability to learn deterministic optimal polices naturally from inference and the ability to optimise value functions and policies in separate, iterative steps. In applying variational expectation-maximisation to VIREL we thus show that the actor-critic algorithm can be reduced to expectation-maximisation... [full abstract]

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators by building on ideas from amortized variational inference. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We further demonstrate the practicality of our approach on a number of end-to-end experiments.

We use Bayesian CNNs and a novel generative model of Galaxy Zoo volunteer responses to infer posteriors for the visual morphology of galaxies. Bayesian CNN can learn from galaxy images with uncertain labels and then, for previously unlabelled galaxies, predict the probability of each possible label. Using our posteriors, we apply the active learning strategy BALD to request volunteer responses for the subset of galaxies which, if labelled, would be most informative for training our network. By combining human and machine intelligence, Galaxy Zoo will be able to classify surveys of any conceivable scale on a timescale of weeks, providing massive and detailed morphology catalogues to support research into galaxy evolution.

Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, exttt{plan-net}, based on an ensemble of Bayesian neural networks that yields more accurate inferences than the random forest for the same data set of synthetic transmission spectra.

Before deploying autonomous agents in the real world, we need to be confident they will perform safely in novel situations. Ideally, we would expose agents to a very wide range of situations during training (e.g. many simulated environments), allowing them to learn about every possible danger. But this is often impractical: simulations may fail to capture the full range of situations and may differ subtly from reality. This paper investigates generalizing from a limited number of training environments in deep reinforcement learning. Our experiments test whether agents can perform safely in novel environments, given varying numbers of environments at train time. Using a gridworld setting, we find that standard deep RL agents do not reliably avoid catastrophes on unseen environments – even after performing near optimally on 1000 training environments. However, we show that catastrophes can be significantly reduced (but not eliminated) with simple modifications, including Q-network... [full abstract]

An ML-based retrieval framework called Intelligent exoplaNet Atmospheric RetrievAl (INARA) that consists of a Bayesian deep learning model for retrieval and a data set of 3,000,000 synthetic rocky exoplanetary spectra generated using the NASA Planetary Spectrum Generator.

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

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 us... [full abstract]

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 re... [full abstract]

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.

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 pri... [full abstract]

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.

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.

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... [full abstract]

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.

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.

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 examp... [full abstract]

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.

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 entropy 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.

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.