The theory of large deviations is concerned with various approximations involving rare
events. It is also concerned with characterizing the circumstances that lead to a given rare …

The zig-zag process is a piecewise deterministic Markov process in position and velocity
space. The process can be designed to have an arbitrary Gibbs type marginal probability …

Metastability is a formidable challenge to Markov chain Monte Carlo methods. In this paper
we present methods for algorithm design to meet this challenge. The design problem we …

Langevin diffusion (LD) is one of the main workhorses for sampling problems. However, its
convergence rate can be significantly reduced if the target distribution is a mixture of multiple …

Sampling Gibbs measures at low temperatures is an important task but computationally
challenging. Numerical evidence suggests that the infinite-swapping algorithm (isa) is a …

Finding equilibria points in continuous minimax games has become a key problem within
machine learning, in part due to its connection to the training of generative adversarial …

To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling
relies on constructing an ergodic Markov chain with the target distribution as its invariant …

Sampling Gibbs measures at low temperatures is an important but computationally
challenging task. Numerical evidence suggests that the infinite-swapping algorithm (isa) is a …

The aim of this paper is to develop tractable large deviation approximations for the empirical
measure of a small noise diffusion. The starting point is the Freidlin–Wentzell theory, which …

Given the important role latent variable models play, for example in statistical learning, there
is currently a growing need for efficient Monte Carlo methods for conducting inference on the …