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Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…
We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin…
Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases…
Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling.…
A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated…
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally…
We extend the L\'evy Langevin Monte Carlo method studied by Oechsler in 2024 to the setting of a target distribution with heavy tails: Choosing a target distribution from the class of subexponential distributions we prove convergence of a…
Studying the subexponential convergence towards equilibrium of a strong Markov process, we exhibit an intermediate Lyapunov condition equivalent to the control of some moment of a hitting time. This provides a link, similar (although more…
This article develops general conditions for weak convergence of adaptive Markov chain Monte Carlo processes and is shown to imply a weak law of large numbers for bounded Lipschitz continuous functions. This allows an estimation theory for…
Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…
Hamiltonian Monte Carlo (HMC) has been widely adopted in the statistics community because of its ability to sample high-dimensional distributions much more efficiently than other Metropolis-based methods. Despite this, HMC often performs…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…