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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., Comment: Published at AISTATS 2023

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes jumps between different dimensional spaces. We first define a dimension destroying forward noising process, before deriving the dimension creating time-reversed generative process along with a novel evidence lower bound training objective for learning to approximate it. Simulating our learned approximation to the time-reversed generative process then provides an effective way of sampling data of varying dimensionality by jointly generating state values and dimensions. We demonstrate our approach on molecular and video datasets of varying dimensionality, reporting better compatibility with test-time diffusion guidance imputation tasks and improved interpolation capabilities versus fixed dimensional models that generate state values and dimensions separately., Comment: 38 pages, 11 figures, 5 tables

We introduce Markov Neural Processes (MNPs), a new class of Stochastic Processes (SPs) which are constructed by stacking sequences of neural parameterised Markov transition operators in function space. We prove that these Markov transition operators can preserve the exchangeability and consistency of SPs. Therefore, the proposed iterative construction adds substantial flexibility and expressivity to the original framework of Neural Processes (NPs) without compromising consistency or adding restrictions. Our experiments demonstrate clear advantages of MNPs over baseline models on a variety of tasks., Comment: 18 pages, 5 figures

We propose Active Surrogate Estimators (ASEs), a new method for label-efficient model evaluation. Evaluating model performance is a challenging and important problem when labels are expensive. ASEs address this active testing problem using a surrogate-based estimation approach that interpolates the errors of points with unknown labels, rather than forming a Monte Carlo estimator. ASEs actively learn the underlying surrogate, and we propose a novel acquisition strategy, XWED, that tailors this learning to the final estimation task. We find that ASEs offer greater label-efficiency than the current state-of-the-art when applied to challenging model evaluation problems for deep neural networks., Comment: Accepted for publication at NeurIPS 2022

We investigate the benefit of treating all the parameters in a Bayesian neural network stochastically and find compelling theoretical and empirical evidence that this standard construction may be unnecessary. To this end, we prove that expressive predictive distributions require only small amounts of stochasticity. In particular, partially stochastic networks with only $n$ stochastic biases are universal probabilistic predictors for $n$-dimensional predictive problems. In empirical investigations, we find no systematic benefit of full stochasticity across four different inference modalities and eight datasets; partially stochastic networks can match and sometimes even outperform fully stochastic networks, despite their reduced memory costs., Comment: Published at AISTATS2023 (Oral)

We introduce InstaAug, a method for automatically learning input-specific augmentations from data. Previous methods for learning augmentations have typically assumed independence between the original input and the transformation applied to that input. This can be highly restrictive, as the invariances we hope our augmentation will capture are themselves often highly input dependent. InstaAug instead introduces a learnable invariance module that maps from inputs to tailored transformation parameters, allowing local invariances to be captured. This can be simultaneously trained alongside the downstream model in a fully end-to-end manner, or separately learned for a pre-trained model. We empirically demonstrate that InstaAug learns meaningful input-dependent augmentations for a wide range of transformation classes, which in turn provides better performance on both supervised and self-supervised tasks.

Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is known that such subsampling operations are not translation equivariant, unlike convolutions that are translation equivariant. Here, we first introduce translation equivariant subsampling/upsampling layers that can be used to construct exact translation equivariant CNNs. We then generalise these layers beyond translations to general groups, thus proposing group equivariant subsampling/upsampling. We use these layers to construct group equivariant autoencoders (GAEs) that allow us to learn low-dimensional equivariant representations. We empirically verify on images that the representations are indeed equivariant to input translations and rotations, and thus generalise well to unseen positions and orientations. We further use GAEs in models that learn object-centric representations on multi-object datasets, and show improved data efficiency and decomposition compared to non-equivariant baselines.

We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substantial computation 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 represents a design policy which 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 that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems., Comment: Published as a conference paper at ICML 2021

We introduce an approach for training Variational Autoencoders (VAEs) that are certifiably robust to adversarial attack. Specifically, we first derive actionable bounds on the minimal size of an input perturbation required to change a VAE's reconstruction by more than an allowed amount, with these bounds depending on certain key parameters such as the Lipschitz constants of the encoder and decoder. We then show how these parameters can be controlled, thereby providing a mechanism to ensure \textit{a priori} that a VAE will attain a desired level of robustness. Moreover, we extend this to a complete practical approach for training such VAEs to ensure our criteria are met. Critically, our method allows one to specify a desired level of robustness \emph{upfront} and then train a VAE that is guaranteed to achieve this robustness. We further demonstrate that these Lipschitz--constrained VAEs are more robust to attack than standard VAEs in practice., Comment: 12 pages and appendix

We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models., Comment: 33 pages, 8 figures. Published as a conference paper at NeurIPS 2021

Expanding on MacKay (1992), we argue that conventional model-based methods for active learning - like BALD - have a fundamental shortfall: they fail to directly account for the test-time distribution of the input variables. This can lead to pathologies in the acquisition strategy, as what is maximally informative for model parameters may not be maximally informative for prediction: for example, when the data in the pool set is more dispersed than that of the final prediction task, or when the distribution of pool and test samples differs. To correct this, we revisit an acquisition strategy that is based on maximizing the expected information gained about possible future predictions, referring to this as the Expected Predictive Information Gain (EPIG). As EPIG does not scale well for batch acquisition, we further examine an alternative strategy, a hybrid between BALD and EPIG, which we call the Joint Expected Predictive Information Gain (JEPIG). We consider using both for active learning with Bayesian neural networks on a variety of datasets, examining the behavior under distribution shift in the pool set.

We propose methods to strengthen the invariance properties of representations obtained by contrastive learning. While existing approaches implicitly induce a degree of invariance as representations are learned, we look to more directly enforce invariance in the encoding process. To this end, we first introduce a training objective for contrastive learning that uses a novel regularizer to control how the representation changes under transformation. We show that representations trained with this objective perform better on downstream tasks and are more robust to the introduction of nuisance transformations at test time. Second, we propose a change to how test time representations are generated by introducing a feature averaging approach that combines encodings from multiple transformations of the original input, finding that this leads to across the board performance gains. Finally, we introduce the novel Spirograph dataset to explore our ideas in the context of a differentiable generative process with multiple downstream tasks, showing that our techniques for learning invariance are highly beneficial., Comment: Published as a conference paper at ICLR 2021

Inference amortization methods share information across multiple posterior-inference problems, allowing each to be carried out more efficiently. Generally, they require the inversion of the dependency structure in the generative model, as the modeller must learn a mapping from observations to distributions approximating the posterior. Previous approaches have involved inverting the dependency structure in a heuristic way that fails to capture these dependencies correctly, thereby limiting the achievable accuracy of the resulting approximations. We introduce an algorithm for faithfully, and minimally, inverting the graphical model structure of any generative model. Such inverses have two crucial properties: (a) they do not encode any independence assertions that are absent from the model and; (b) they are local maxima for the number of true independencies encoded. We prove the correctness of our approach and empirically show that the resulting minimally faithful inverses lead to better inference amortization than existing heuristic approaches., Comment: To appear at the 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), Montreal, Canada

Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being generated by an explicit adversary, while the poor train--test generalization of adversarial metrics can limit their usage to simple problems. Motivated by this, we develop a probabilistic robust risk framework, the statistically robust risk (SRR), which considers pointwise corruption distributions, as opposed to worst-case adversaries. The SRR provides a distinct and complementary measure of robust performance, compared to natural and adversarial risk. We show that the SRR admits estimation and training schemes which are as simple and efficient as for the natural risk: these simply require noising the inputs, but with a principled derivation for exactly how and why this should be done. Furthermore, we demonstrate both theoretically and experimentally that it can provide superior generalization performance compared with adversarial risks, enabling application to high-dimensional datasets., Comment: UAI 2021

Epidemiology simulations have become a fundamental tool in the fight against the epidemics of various infectious diseases like AIDS and malaria. However, the complicated and stochastic nature of these simulators can mean their output is difficult to interpret, which reduces their usefulness to policymakers. In this paper, we introduce an approach that allows one to treat a large class of population-based epidemiology simulators as probabilistic generative models. This is achieved by hijacking the internal random number generator calls, through the use of a universal probabilistic programming system (PPS). In contrast to other methods, our approach can be easily retrofitted to simulators written in popular industrial programming frameworks. We demonstrate that our method can be used for interpretable introspection and inference, thus shedding light on black-box simulators. This reinstates much-needed trust between policymakers and evidence-based methods., Comment: 6 pages, 3 figures, Accepted at the International Conference on Machine Learning AI for Social Good Workshop, Long Beach, United States, 2019

Imagine a world where computational simulations can be inverted as easily as running them forwards, where data can be used to refine models automatically, and where the only expertise one needs to carry out powerful statistical analysis is a basic proficiency in scientific coding. Creating such a world is the ambitious long-term aim of probabilistic programming. The bottleneck for improving the probabilistic models, or simulators, used throughout the quantitative sciences, is often not an ability to devise better models conceptually, but a lack of expertise, time, or resources to realize such innovations. Probabilistic programming systems (PPSs) help alleviate this bottleneck by providing an expressive and accessible modeling framework, then automating the required computation to draw inferences from the model, for example finding the model parameters likely to give rise to a certain output. By decoupling model specification and inference, PPSs streamline the process of developing and drawing inferences from new models, while opening up powerful statistical methods to non-experts. Many systems further provide the flexibility to write new and exciting models which would be hard, or even impossible, to convey using conventional statistical frameworks. The central goal of this thesis is to improve and extend PPSs. In particular, we will make advancements to the underlying inference engines and increase the range of problems which can be tackled. For example, we will extend PPSs to a mixed inference-optimization framework, thereby providing automation of tasks such as model learning and engineering design. Meanwhile, we make inroads into constructing systems for automating adaptive sequential design problems, providing potential applications across the sciences. Furthermore, the contributions of the work reach far beyond probabilistic programming, as achieving our goal will require us to make advancements in a number of related fields such as particle Markov chain Monte Carlo methods, Bayesian optimization, and Monte Carlo fundamentals.

We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification framework in that when the property can be violated, it provides an informative notion of how robust the network is, rather than just the conventional assertion that the network is not verifiable. Furthermore, it provides an ability to scale to larger networks than formal verification approaches. Though the framework still provides a formal guarantee of satisfiability whenever it successfully finds one or more violations, these advantages do come at the cost of only providing a statistical estimate of unsatisfiability whenever no violation is found. Key to the practical success of our approach is an adaptation of multi-level splitting, a Monte Carlo approach for estimating the probability of rare events, to our statistical robustness framework. We demonstrate that our approach is able to emulate formal verification procedures on benchmark problems, while scaling to larger networks and providing reliable additional information in the form of accurate estimates of the violation probability., Comment: To appear at the 7th International Conference on Learning Representations (ICLR 2019), New Orleans

We study adaptive importance sampling (AIS) as an online learning problem and argue for the importance of the trade-off between exploration and exploitation in this adaptation. Borrowing ideas from the bandits literature, we propose Daisee, a partition-based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has $\mathcal{O}(\sqrt{T}(\log T)^{\frac{3}{4}})$ cumulative pseudo-regret, where $T$ is the number of iterations. We then extend Daisee to adaptively learn a hierarchical partitioning of the sample space for more efficient sampling and confirm the performance of both algorithms empirically.

Hamiltonian Monte Carlo (HMC) is arguably the dominant statistical inference algorithm used in most popular "first-order differentiable" Probabilistic Programming Languages (PPLs). However, the fact that HMC uses derivative information causes complications when the target distribution is non-differentiable with respect to one or more of the latent variables. In this paper, we show how to use extensions to HMC to perform inference in probabilistic programs that contain discontinuities. To do this, we design a Simple first-order Probabilistic Programming Language (SPPL) that contains a sufficient set of language restrictions together with a compilation scheme. This enables us to preserve both the statistical and syntactic interpretation of if-else statements in the probabilistic program, within the scope of first-order PPLs. We also provide a corresponding mathematical formalism that ensures any joint density denoted in such a language has a suitably low measure of discontinuities., Comment: 4 pages, 2 figures

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering significant performance improvements over prominent existing packages. We present applications of our method to a number of tasks including engineering design and parameter optimization.

We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in structured probabilistic models and the flexibility of deep neural networks to model complex conditional probability distributions. We develop additional theoretical insights and introduce a new training procedure which improves both model and proposal learning. We demonstrate that our approach provides a fast, easy-to-implement and scalable means for simultaneous model learning and proposal adaptation in deep generative models.

Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistical implications of nesting MC estimators, including cases of multiple levels of nesting, and establish the conditions under which they converge. We derive corresponding rates of convergence and provide empirical evidence that these rates are observed in practice. We further establish a number of pitfalls that can arise from naive nesting of MC estimators, provide guidelines about how these can be avoided, and lay out novel methods for reformulating certain classes of nested expectation problems into single expectations, leading to improved convergence rates. We demonstrate the applicability of our work by using our results to develop a new estimator for discrete Bayesian experimental design problems and derive error bounds for a class of variational objectives., Comment: To appear at International Conference on Machine Learning 2018

Delayed and risky choice (DARC) experiments are a cornerstone of research in psychology, behavioural economics and neuroeconomics. By collecting an agent's preferences between pairs of prospects we can characterise their preferences, investigate what affects them, and probe the underlying decision making mechanisms. We present a state-of-the-art approach and software toolbox allowing such DARC experiments to be run in a highly efficient way. Data collection is costly, so our toolbox automatically and adaptively generates pairs of prospects in real time to maximise the information gathered about the participant's behaviours. We demonstrate that this leads to improvements over alternative experimental paradigms. The key to releasing our real time and automatic performance is a number of advances over current Bayesian adaptive design methodology. In particular, we derive an improved estimator for discrete output problems and design a novel algorithm for automating sequential adaptive design. We provide a number of pre-prepared DARC tools for researchers to use, but a key contribution is an adaptive experiment toolbox that can be extended to virtually any 2-alternative-choice tasks. In particular, to carry out custom adaptive experiments using our toolbox, the user need only encode their behavioural model and design space - both the subsequent inference and sequential design optimisation are automated for arbitrary models the user might write.

There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for which classical convergence proofs are insufficient. We give conditions under which NMC will converge, establish a rate of convergence, and provide empirical data that suggests that this rate is observable in practice. Finally, we prove that general-purpose nested inference schemes are inherently biased. Our results serve to warn of the dangers associated with naive composition of inference and models., Comment: Appearing in NIPS Workshop on Advances in Approximate Bayesian Inference 2016

Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restricts the space of possible solutions and leads to over-confident uncertainty estimates. We introduce a fully Bayesian approach, inferring a full posterior over structures, which more reliably captures the uncertainty of the model.