It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is based in large part on the unifying concept of tensors, we describe a software abstraction --functional tensors-- that captures many of the benefits of tensors, while also being able to describe continuous probability distributions. Moreover, functional tensors are a natural candidate for generalized variable elimination and parallel-scan filtering algorithms that enable parallel exact inference for a large family of tractable modeling motifs. We demonstrate the versatility of functional tensors by integrating them into the modeling frontend and inference backend of the Pyro programming language. In experiments we show that the resulting framework enables a large variety of inference strategies, including those that mix exact and approximate inference.

Neural Network based controllers hold enormous potential to learn complex, high-dimensional functions. However, they are prone to overfitting and unwarranted extrapolations. PAC Bayes is a generalized framework which is more resistant to overfitting and that yields performance bounds that hold with arbitrarily high probability even on the unjustified extrapolations. However, optimizing to learn such a function and a bound is intractable for complex tasks. In this work, we propose a method to simultaneously learn such a function and estimate performance bounds that scale organically to high-dimensions, non-linear environments without making any explicit assumptions about the environment. We build our approach on a parallel that we draw between the formulations called ELBO and PAC Bayes when the risk metric is negative log likelihood. Through our experiments on multiple high dimensional MuJoCo locomotion tasks, we validate the correctness of our theory, show its ability to generalize better, and investigate the factors that are important for its learning. The code for all the experiments is available at https://bit.ly/2qv0JjA.

Marta Kwiatkowska is a co-proposer of the Validate AI Conference. She is Professor of Computing Systems and Fellow of Trinity College, University of Oxford. Prior to this she was Professor in the School of Computer Science at the University of Birmingham, Lecturer at the University of Leicester and Assistant Professor at the Jagiellonian University in Cracow, Poland. Kwiatkowska has made fundamental contributions to the theory and practice of model checking for probabilistic systems, focusing on automated techniques for verification and synthesis from quantitative specifications. More recently, she has been working on safety and robustness verification for neural networks with provable guarantees.

Marta Kwiatkowska is a co-proposer of the Validate AI Conference. She is Professor of Computing Systems and Fellow of Trinity College, University of Oxford. Prior to this she was Professor in the School of Computer Science at the University of Birmingham, Lecturer at the University of Leicester and Assistant Professor at the Jagiellonian University in Cracow, Poland. Kwiatkowska has made fundamental contributions to the theory and practice of model checking for probabilistic systems, focusing on automated techniques for verification and synthesis from quantitative specifications. More recently, she has been working on safety and robustness verification for neural networks with provable guarantees.

We develop a generative model-based approach to Bayesian inverse problems, such as image reconstruction from noisy and incomplete images. Our framework addresses two common challenges of Bayesian reconstructions: 1) It makes use of complex, data-driven priors that comprise all available information about the uncorrupted data distribution. 2) It enables computationally tractable uncertainty quantification in the form of posterior analysis in latent and data space. The method is very efficient in that the generative model only has to be trained once on an uncorrupted data set, after that, the procedure can be used for arbitrary corruption types.

The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from uncontrolled data have been proposed. However, most of these deal only with purely directed causal relationships and cannot detect latent common causes. Here, we devise a general method which takes a purely directed causal discovery algorithm and modifies it so that it can also detect latent common causes. The identifiability of the modified algorithm depends on the identifiability of the original, as well as an assumption that the strength of noise be relatively small. We apply our method to two directed causal discovery algorithms, the Information Geometric Causal Inference of (Daniusis et al., 2010) and the Kernel Conditional Deviance for Causal Inference of (Mitrovic, Sejdinovic, and Teh, 2018), and extensively test on synthetic data---detecting latent common causes in additive, multiplicative and complex noise regimes---and on real data, where we are able to detect known common causes. In addition to detecting latent common causes, our experiments demonstrate that both modified algorithms preserve the performance of the original directed algorithm in distinguishing directed causal relations.

Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving approximate inference over the latent variables by minimizing a tight upper bound on the approximation gap. Given a discrete latent variable $Z$, the proposed approximation reduces inference complexity from $O(|Z|^c)$ to $O(|Z|)$. We use convex conjugates to determine this upper bound in a closed form and show that its addition to the optimization objective results in improved results for models assuming proportional hazards as in Survival Analysis.

Change-point detection (CPD) aims to locate abrupt transitions in the generative model of a sequence of observations. When Bayesian methods are considered, the standard practice is to infer the posterior distribution of the change-point locations. However, for complex models (high-dimensional or heterogeneous), it is not possible to perform reliable detection. To circumvent this problem, we propose to use a hierarchical model, which yields observations that belong to a lower-dimensional manifold. Concretely, we consider a latent-class model with an unbounded number of categories, which is based on the chinese-restaurant process (CRP). For this model we derive a continual learning mechanism that is based on the sequential construction of the CRP and the expectation-maximization (EM) algorithm with a stochastic maximization step. Our results show that the proposed method is able to recursively infer the number of underlying latent classes and perform CPD in a reliable manner.

The aim of clinical effectiveness research using repositories of electronic health records is to identify what health interventions 'work best' in real-world settings. Since there are several reasons why the net benefit of intervention may differ across patients, current comparative effectiveness literature focuses on investigating heterogeneous treatment effect and predicting whether an individual might benefit from an intervention. The majority of this literature has concentrated on the estimation of the effect of treatment on binary outcomes. However, many medical interventions are evaluated in terms of their effect on future events, which are subject to loss to follow-up. In this study, we describe a framework for the estimation of heterogeneous treatment effect in terms of differences in time-to-event (survival) probabilities. We divide the problem into three phases: (1) estimation of treatment effect conditioned on unique sets of the covariate vector; (2) identification of features important for heterogeneity using an ensemble of non-parametric variable importance methods; and (3) estimation of treatment effect on the reference classes defined by the previously selected features, using one-step Targeted Maximum Likelihood Estimation. We conducted a series of simulation studies and found that this method performs well when either sample size or event rate is high enough and the number of covariates contributing to the effect heterogeneity is moderate. An application of this method to a clinical case study was conducted by estimating the effect of oral anticoagulants on newly diagnosed non-valvular atrial fibrillation patients using data from the UK Clinical Practice Research Datalink.

Markov chain Monte Carlo (MCMC) methods and neural networks are instrumental in tackling inferential and prediction problems. However, Bayesian inference based on joint use of MCMC methods and of neural networks is limited. This paper reviews the main challenges posed by neural networks to MCMC developments, including lack of parameter identifiability due to weight symmetries, prior specification effects, and consequently high computational cost and convergence failure. Population and manifold MCMC algorithms are combined to demonstrate these challenges via multilayer perceptron (MLP) examples and to develop case studies for assessing the capacity of approximate inference methods to uncover the posterior covariance of neural network parameters. Some of these challenges, such as high computational cost arising from the application of neural networks to big data and parameter identifiability arising from weight symmetries, stimulate research towards more scalable approximate MCMC methods or towards MCMC methods in reduced parameter spaces.