Related papers: Improving the convergence of reversible samplers
We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…
The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…
A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a…
Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered…
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings,…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…
Reversible Markov chains play a central role in stochastic modelling and in algorithms such as Markov chain Monte Carlo (MCMC). Motivated by the fundamental importance of reversibility in classical settings, this paper develops a…
We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the…
MCMC methods (Monte Carlo Markov Chain) are a class of methods used to perform simulations per a probability distribution $P$. These methods are often used when we have difficulties to directly sample per a given probability distribution…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
Markov chain Monte Carlo is widely used in a variety of scientific applications to generate approximate samples from intractable distributions. A thorough understanding of the convergence and mixing properties of these Markov chains can be…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…