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We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the…

We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly…

Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…

State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time…

Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC…

Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology…

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…

This paper presents a stochastic model predictive control (SMPC) algorithm for linear systems subject to additive Gaussian mixture disturbances, with the goal of satisfying chance constraints. We focus on a special case where each Gaussian…

Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…

Approximate inference in complex probabilistic models such as deep Gaussian processes requires the optimisation of doubly stochastic objective functions. These objectives incorporate randomness both from mini-batch subsampling of the data…

Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control…

Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…

Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial…

We consider the stochastic gradient descent (SGD) algorithm driven by a general stochastic sequence, including i.i.d noise and random walk on an arbitrary graph, among others; and analyze it in the asymptotic sense. Specifically, we employ…

To detect changes in the mean of a time series, one may use previsible detection procedures based on nonparametric kernel prediction smoothers which cover various classic detection statistics as special cases. Bandwidth selection,…

Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…

We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models (DGMs) in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly…

A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…

Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo (MCMC) with simple proposal mechanisms. This hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper,…

We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics.…