Related papers: Reverse Diffusion Monte Carlo

The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating…

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…

Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

In this article, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag…

We present Diffusion Restore, a real-time framework for diffusion-based MCMC light transport. MCMC methods are highly suitable for sampling from complex high-dimensional distributions and for approximating integrals over them. In practice,…

Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…

Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…

Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges…

Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…

It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers…

The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…

In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach…

We address the challenge of training diffusion models to sample from unnormalized energy distributions in the absence of data, the so-called diffusion samplers. Although these approaches have shown promise, they struggle to scale in more…

This paper is concerned with differentiable resampling in the context of sequential Monte Carlo (e.g., particle filtering). Drawing on reparametrisation, we propose a new resampling method that is informative and instantly differentiable,…

Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a…

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…