We present the Sum-Product Probabilistic Language (SPPL), a new system that automatically delivers exact solutions to a broad range of probabilistic inference queries. SPPL symbolically represents the full distribution on execution traces specified by a probabilistic program using a generalization of sum-product networks. SPPL handles continuous and discrete distributions, many-to-one numerical transformations, and a query language that includes general predicates on random variables. We formalize SPPL in terms of a novel translation strategy from probabilistic programs to a semantic domain of sum-product representations, present new algorithms for exactly conditioning on and computing probabilities of queries, and prove their soundness under the semantics. We present techniques for improving the scalability of translation and inference by automatically exploiting conditional independences and repeated structure in SPPL programs. We implement a prototype of SPPL with a modular architecture and evaluate it on a suite of common benchmarks, which establish that our system is up to 3500x faster than state-of-the-art systems for fairness verification; up to 1000x faster than state-of-the-art symbolic algebra techniques; and can compute exact probabilities of rare events in milliseconds.

We propose a novel data-driven approach to solving a classical statistical mechanics problem: given data on collective motion of particles, characterise the set of free energies associated with the system of particles. We demonstrate empirically that the particle data contains all the information necessary to infer a free energy. While traditional physical modelling seeks to construct analytically tractable approximations, the proposed approach leverages modern Bayesian computational capabilities to accomplish this in a purely data-driven fashion. The Bayesian paradigm permits us to combine underpinning physical principles with simulation data to obtain uncertainty-quantified predictions of the free energy, in the form of a probability distribution over the family of free energies consistent with the observed particle data. In the present work we focus on classical statistical mechanical systems with excluded volume interactions. Using standard coarse-graining methods, our results can be made applicable to systems with realistic attractive-repulsive interactions. We validate our method on a paradigmatic and computationally cheap case of a one-dimensional fluid. With the appropriate particle data, it is possible to learn canonical and grand-canonical representations of the underlying physical system. Extensions to higher-dimensional systems are conceptually straightforward.

Bayesian bandits using Thompson Sampling have seen increasing success in recent years. Yet existing value models (of rewards) are misspecified on many real-world problem. We demonstrate this on the User Experience Optimization (UXO) problem, providing a novel formulation as a restless, sleeping bandit with unobserved confounders plus optional stopping. Our case studies show how common misspecifications can lead to sub-optimal rewards, and we provide model extensions to address these, along with a scientific model building process practitioners can adopt or adapt to solve their own unique problems. To our knowledge, this is the first study showing the effects of overdispersion on bandit explore/exploit efficacy, tying the common notions of under- and over-confidence to over- and under-exploration, respectively. We also present the first model to exploit cointegration in a restless bandit, demonstrating that finite regret and fast and consistent optional stopping are possible by moving beyond simpler windowing, discounting, and drift models.

Distance weighted discrimination (DWD) is a linear discrimination method that is particularly well-suited for classification tasks with high-dimensional data. The DWD coefficients minimize an intuitive objective function, which can solved very efficiently using state-of-the-art optimization techniques. However, DWD has not yet been cast into a model-based framework for statistical inference. In this article we show that DWD identifies the mode of a proper Bayesian posterior distribution, that results from a particular link function for the class probabilities and a shrinkage-inducing proper prior distribution on the coefficients. We describe a relatively efficient Markov chain Monte Carlo (MCMC) algorithm to simulate from the true posterior under this Bayesian framework. We show that the posterior is asymptotically normal and derive the mean and covariance matrix of its limiting distribution. Through several simulation studies and an application to breast cancer genomics we demonstrate how the Bayesian approach to DWD can be used to (1) compute well-calibrated posterior class probabilities, (2) assess uncertainty in the DWD coefficients and resulting sample scores, (3) improve power via semi-supervised analysis when not all class labels are available, and (4) automatically determine a penalty tuning parameter within the model-based framework. R code to perform Bayesian DWD is available at https://github.com/lockEF/BayesianDWD .

Approximate Bayesian methods can mitigate overconfidence in ReLU networks. However, far away from the training data, even Bayesian neural networks (BNNs) can still underestimate uncertainty and thus be overconfident. We suggest to fix this by considering an infinite number of ReLU features over the input domain that are never part of the training process and thus remain at prior values. Perhaps surprisingly, we show that this model leads to a tractable Gaussian process (GP) term that can be added to a pre-trained BNN's posterior at test time with negligible cost overhead. The BNN then yields structured uncertainty in the proximity of training data, while the GP prior calibrates uncertainty far away from them. As a key contribution, we prove that the added uncertainty yields cubic predictive variance growth, and thus the ideal uniform (maximum entropy) confidence in multi-class classification far from the training data. Calibrated uncertainty is crucial for safety-critical decision making by neural networks (NNs) (Amodei et al., 2016). Standard training methods of NNs yield point estimates that, even if they are highly accurate, can still be severely overconfident (Guo et al., 2017).

We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any subset of observations. Our framework allows for regression, classification and heterogeneous tasks, i.e. mix of continuous and discrete variables over the same input domain. We exploit infinite-dimensional integral operators based on the Kullback-Leibler divergence between stochastic processes to re-combine arbitrary amounts of variational sparse approximations with different complexity, likelihood model and location of the pseudo-inputs. Extensive results illustrate the usability of our framework in large-scale distributed experiments, also compared with the exact inference models in the literature.

Density estimation, compression and data generation are crucial tasks in artificial intelligence. Variational Auto-Encoders (VAEs) constitute a single framework to achieve these goals. Here, we present a novel class of generative models, called self-supervised Variational Auto-Encoder (selfVAE), that utilizes deterministic and discrete variational posteriors. This class of models allows to perform both conditional and unconditional sampling, while simplifying the objective function. First, we use a single self-supervised transformation as a latent variable, where a transformation is either downscaling or edge detection. Next, we consider a hierarchical architecture, i.e., multiple transformations, and we show its benefits compared to the VAE. The flexibility of selfVAE in data reconstruction finds a particularly interesting use case in data compression tasks, where we can trade-off memory for better data quality, and vice-versa. We present performance of our approach on three benchmark image data (Cifar10, Imagenette64, and CelebA).

We introduce a framework for online changepoint detection and simultaneous model learning which is applicable to highly parametrized models, such as deep neural networks. It is based on detecting changepoints across time by sequentially performing generalized likelihood ratio tests that require only evaluations of simple prediction score functions. This procedure makes use of checkpoints, consisting of early versions of the actual model parameters, that allow to detect distributional changes by performing predictions on future data. We define an algorithm that bounds the Type I error in the sequential testing procedure. We demonstrate the efficiency of our method in challenging continual learning applications with unknown task changepoints, and show improved performance compared to online Bayesian changepoint detection.

Fast machine learning-based surrogate models are trained to emulate slow, high-fidelity engineering simulation models to accelerate engineering design tasks. This introduces uncertainty as the surrogate is only an approximation of the original model. Bayesian methods can quantify that uncertainty, and deep learning models exist that follow the Bayesian paradigm. These models, namely Bayesian neural networks and Gaussian process models, enable us to give predictions together with an estimate of the model's uncertainty. As a result we can derive uncertainty-aware surrogate models that can automatically suspect unseen design samples that cause large emulation errors. For these samples, the high-fidelity model can be queried instead. This outlines how the Bayesian paradigm allows us to hybridize fast, but approximate, and slow, but accurate models. In this paper, we train two types of Bayesian models, dropout neural networks and stochastic variational Gaussian Process models, to emulate a complex high dimensional building energy performance simulation problem. The surrogate model processes 35 building design parameters (inputs) to estimate 12 different performance metrics (outputs). We benchmark both approaches, prove their accuracy to be competitive, and show that errors can be reduced by up to 30% when the 10% of samples with the highest uncertainty are transferred to the high-fidelity model.

Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual information. Although showing promise for this difficult problem, the variational methods have been theoretically and empirically proven to have serious statistical limitations: 1) many methods struggle to produce accurate estimates when the underlying mutual information is either low or high; 2) the resulting estimators may suffer from high variance. Our approach is based on training a classifier that provides the probability that a data sample pair is drawn from the joint distribution rather than from the product of its marginal distributions. Moreover, we establish a direct connection between mutual information and the average log odds estimate produced by the classifier on a test set, leading to a simple and accurate estimator of mutual information. We show theoretically that our method and other variational approaches are equivalent when they achieve their optimum, while our method sidesteps the variational bound. Empirical results demonstrate high accuracy of our approach and the advantages of our estimator in the context of representation learning. Mutual information (MI) measures the information that two random variables share.