A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of the corresponding row and column of the graph affinity matrix, a latent state of SGLDS can be categorized as either a non-dynamic state or a dynamic one. A normal-gamma construction is used to shrink the energy captured by the non-dynamic states, while the dynamic states can be further categorized into live, absorbing, or noise-injection states, which capture different types of dynamical components of the underlying time series. The state-of-the-art performance of SGLDS is demonstrated with experiments on both synthetic and real data.

Bayesian neural networks with latent variables (BNNs LVs) are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, they can capture complex noise patterns in the data. In this work, we show how to separate these two forms of uncertainty for decision-making purposes. This decomposition allows us to successfully identify informative points for active learning of functions with heteroskedastic and bimodal noise. We also demonstrate how this decomposition allows us to define a novel risk-sensitive reinforcement learning criterion to identify policies that balance expected cost, model-bias and noise averseness.

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the variational sequential Monte Carlo (VSMC) family, and show how to optimize it in variational inference. VSMC melds variational inference (VI) and sequential Monte Carlo (SMC), providing practitioners with flexible, accurate, and powerful Bayesian inference. The VSMC family is a variational family that can approximate the posterior arbitrarily well, while still allowing for efficient optimization of its parameters. We demonstrate its utility on state space models, stochastic volatility models for financial data, and deep Markov models of brain neural circuits.

We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density \wrt\ the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization factor $x \mapsto \pi(x)= \mathrm{e}^{-U(x)}/\int_{\mathbb{R}^d} \mathrm{e}^{-U(y)} \mathrm{d}y$. Such problem naturally occurs for example in Bayesian inference and machine learning. Under the assumption that $U$ is continuously differentiable, $\nabla U$ is globally Lipschitz and $U$ is strongly convex, we obtain non-asymptotic bounds for the convergence to stationarity in Wasserstein distance of order $2$ and total variation distance of the sampling method based on the Euler discretization of the Langevin stochastic differential equation, for both constant and decreasing step sizes. The dependence on the dimension of the state space of the obtained bounds is studied to demonstrate the applicability of this method. The convergence of an appropriately weighted empirical measure is also investigated and bounds for the mean square error and exponential deviation inequality are reported for functions which are measurable and bounded. An illustration to Bayesian inference for binary regression is presented.

Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discrete graphical models. In order to avoid the canonical, yet prohibitive, Cholesky $\mathcal{O}(n^{3})$ computational cost, we propose a novel approach, with complexity $\mathcal{O}(n^{2})$, based on a constrained variational Bayes algorithm. We compare our method to Taylor, Chebyshev and Lanczos approaches and show state of the art performance on both synthetic and real-world datasets.

We present the first class of policy-gradient algorithms that work with both state-value and policy function-approximation, and are guaranteed to converge under off-policy training. Our solution targets problems in reinforcement learning where the action representation adds to the-curse-of-dimensionality; that is, with continuous or large action sets, thus making it infeasible to estimate state-action value functions (Q functions). Using state-value functions helps to lift the curse and as a result naturally turn our policy-gradient solution into classical Actor-Critic architecture whose Actor uses state-value function for the update. Our algorithms, Gradient Actor-Critic and Emphatic Actor-Critic, are derived based on the exact gradient of averaged state-value function objective and thus are guaranteed to converge to its optimal solution, while maintaining all the desirable properties of classical Actor-Critic methods with no additional hyper-parameters. To our knowledge, this is the first time that convergent off-policy learning methods have been extended to classical Actor-Critic methods with function approximation.

Clinical prognostic models derived from largescale healthcare data can inform critical diagnostic and therapeutic decisions. To enable off-theshelf usage of machine learning (ML) in prognostic research, we developed AUTOPROGNOSIS: a system for automating the design of predictive modeling pipelines tailored for clinical prognosis. AUTOPROGNOSIS optimizes ensembles of pipeline configurations efficiently using a novel batched Bayesian optimization (BO) algorithm that learns a low-dimensional decomposition of the pipelines high-dimensional hyperparameter space in concurrence with the BO procedure. This is achieved by modeling the pipelines performances as a black-box function with a Gaussian process prior, and modeling the similarities between the pipelines baseline algorithms via a sparse additive kernel with a Dirichlet prior. Meta-learning is used to warmstart BO with external data from similar patient cohorts by calibrating the priors using an algorithm that mimics the empirical Bayes method. The system automatically explains its predictions by presenting the clinicians with logical association rules that link patients features to predicted risk strata. We demonstrate the utility of AUTOPROGNOSIS using 10 major patient cohorts representing various aspects of cardiovascular patient care.

We consider the forecast aggregation problem in repeated settings, where the forecasts are done on a binary event. At each period multiple experts provide forecasts about an event. The goal of the aggregator is to aggregate those forecasts into a subjective accurate forecast. We assume that experts are Bayesian; namely they share a common prior, each expert is exposed to some evidence, and each expert applies Bayes rule to deduce his forecast. The aggregator is ignorant with respect to the information structure (i.e., distribution over evidence) according to which experts make their prediction. The aggregator observes the experts' forecasts only. At the end of each period the actual state is realized. We focus on the question whether the aggregator can learn to aggregate optimally the forecasts of the experts, where the optimal aggregation is the Bayesian aggregation that takes into account all the information (evidence) in the system. We consider the class of partial evidence information structures, where each expert is exposed to a different subset of conditionally independent signals. Our main results are positive; We show that optimal aggregation can be learned in polynomial time in a quite wide range of instances of the partial evidence environments. We provide a tight characterization of the instances where learning is possible and impossible.

Most methods for learning causal structures from non-experimental data rely on some assumptions of simplicity, the most famous of which is known as the Faithfulness condition. Without assuming such conditions to begin with, we develop a learning theory for inferring the structure of a causal Bayesian network, and we use the theory to provide a novel justification of a certain assumption of simplicity that is closely related to Faithfulness. Here is the idea. With only the Markov and IID assumptions, causal learning is notoriously too hard to achieve statistical consistency but we show that it can still achieve a quite desirable "combined" mode of stochastic convergence to the truth: having almost sure convergence to the true causal hypothesis with respect to almost all causal Bayesian networks, together with a certain kind of locally uniform convergence. Furthermore, every learning algorithm achieving at least that joint mode of convergence has this property: having stochastic convergence to the truth with respect to a causal Bayesian network $N$ only if $N$ satisfies a certain variant of Faithfulness, known as Pearl's Minimality condition---as if the learning algorithm were designed by assuming that condition. This explains, for the first time, why it is not merely optional but mandatory to assume the Minimality condition---or to proceed as if we assumed it.

Bayesian optimization (BO) is a popular technique for sequential black-box function optimization, with applications including parameter tuning, robotics, environmental monitoring, and more. One of the most important challenges in BO is the development of algorithms that scale to high dimensions, which remains a key open problem despite recent progress. In this paper, we consider the approach of Kandasamy et al. (2015), in which the high-dimensional function decomposes as a sum of lower-dimensional functions on subsets of the underlying variables. In particular, we significantly generalize this approach by lifting the assumption that the subsets are disjoint, and consider additive models with arbitrary overlap among the subsets. By representing the dependencies via a graph, we deduce an efficient message passing algorithm for optimizing the acquisition function. In addition, we provide an algorithm for learning the graph from samples based on Gibbs sampling. We empirically demonstrate the effectiveness of our methods on both synthetic and real-world data.