Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of
probability distributions commonly encountered in modern applications. For MCMC …

We study the problem of sampling from a strongly log-concave density supported on
$\mathbb {R}^ d $, and prove a non-asymptotic upper bound on the mixing time of the …

Optimization algorithms and Monte Carlo sampling algorithms have provided the
computational foundations for the rapid growth in applications of statistical machine learning …

Langevin diffusion processes and their discretizations are often used for sampling from a
target density. The most convenient framework for assessing the quality of such a sampling …

We study the problem of sampling from a distribution $ p^*(x)\propto\exp\left (-U (x)\right) $,
where the function $ U $ is $ L $-smooth everywhere and $ m $-strongly convex outside a …

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 …

Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of
integrals as the number of iterations goes to∞. MCMC estimators are generally biased after …

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 obtain several quantitative bounds on the mixing properties of an “ideal” Hamiltonian
Monte Carlo (HMC) Markov chain for a strongly log-concave target distribution π on R d. Our …

We propose a new concept of lifts of reversible diffusion processes and show that various
well-known non-reversible Markov processes arising in applications are lifts in this sense of …