Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of these models has been largely overlooked. The purpose of this work is to study the general properties of this quantity and to show how they can be leveraged in practice. We focus on important inferential problems that rely on the likelihood: estimation and missing data imputation. First, we investigate maximum likelihood estimation for DLVMs: in particular, we show that most unconstrained models used for continuous data have an unbounded likelihood function.

We propose Confusions over Time (CoT), a novel generative framework which facilitates a multi-granular analysis of the decision making process. The CoT not only models the confusions or error properties of individual decision makers and their evolution over time, but also allows us to obtain diagnostic insights into the collective decision making process in an interpretable manner. Interpretable insights are obtained by grouping similar decision makers (and items being judged) into clusters and representing each such cluster with an appropriate prototype and identifying the most important features characterizing the cluster via a subspace feature indicator vector. Experimentation with real world data on bail decisions, asthma treatments, and insurance policy approval decisions demonstrates that CoT can accurately model and explain the confusions of decision makers and their evolution over time. Papers published at the Neural Information Processing Systems Conference.

When observing task demonstrations, human apprentices are able to identify whether a given task is executed correctly long before they gain expertise in actually performing that task. Prior research into learning from demonstrations (LfD) has failed to capture this notion of the acceptability of an execution; meanwhile, temporal logics provide a flexible language for expressing task specifications. Inspired by this, we present Bayesian specification inference, a probabilistic model for inferring task specification as a temporal logic formula. We incorporate methods from probabilistic programming to define our priors, along with a domain-independent likelihood function to enable sampling-based inference. We demonstrate the efficacy of our model for inferring true specifications with over 90% similarity between the inferred specification and the ground truth, both within a synthetic domain and a real-world table setting task.

We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in the models from known upper-bounds on the intractable log-partition function. We show that the bound based on separable optimization on the base polytope of the submodular function is always inferior to a bound based on perturb-and-MAP'' ideas. Then, to learn parameters, given that our approximation of the log-partition function is an expectation (over our own randomization), we use a stochastic subgradient technique to maximize a lower-bound on the log-likelihood.

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo.

Bayesian nonparametric methods based on the Dirichlet process (DP), gamma process and beta process, have proven effective in capturing aspects of various datasets arising in machine learning. However, it is now recognized that such processes have their limitations in terms of the ability to capture power law behavior. As such there is now considerable interest in models based on the Stable Processs (SP), Generalized Gamma process (GGP) and Stable-beta process (SBP). In analogy to tractable processes such as the finite-dimensional Dirichlet process, we describe a class of random processes, we call iid finite-dimensional BFRY processes, that enables one to begin to develop efficient posterior inference algorithms such as variational Bayes that readily scale to massive datasets. For illustrative purposes, we describe a simple variational Bayes algorithm for normalized SP mixture models, and demonstrate its usefulness with experiments on synthetic and real-world datasets. Papers published at the Neural Information Processing Systems Conference.

Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes.

Statistical relational models provide compact encodings of probabilistic dependencies in relational domains, but result in highly intractable graphical models. The goal of lifted inference is to carry out probabilistic inference without needing to reason about each individual separately, by instead treating exchangeable, undistinguished objects as a whole. In this paper, we study the domain recursion inference rule, which, despite its central role in early theoretical results on domain-lifted inference, has later been believed redundant. We show that this rule is more powerful than expected, and in fact significantly extends the range of models for which lifted inference runs in time polynomial in the number of individuals in the domain. This includes an open problem called S4, the symmetric transitivity model, and a first-order logic encoding of the birthday paradox.

In this work, we propose an infinite restricted Boltzmann machine (RBM), whose maximum likelihood estimation (MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization. Papers published at the Neural Information Processing Systems Conference.

We introduce a new sequential Monte Carlo algorithm we call the particle cascade. The particle cascade is an asynchronous, anytime alternative to traditional sequential Monte Carlo algorithms that is amenable to parallel and distributed implementations. It uses no barrier synchronizations which leads to improved particle throughput and memory efficiency. It is an anytime algorithm in the sense that it can be run forever to emit an unbounded number of particles while keeping within a fixed memory budget. We prove that the particle cascade provides an unbiased marginal likelihood estimator which can be straightforwardly plugged into existing pseudo-marginal methods.