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Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from…

Strongly Rayleigh distributions are natural generalizations of product and determinantal probability distributions and satisfy strongest form of negative dependence properties. We show that the "natural" Monte Carlo Markov Chain (MCMC) is…

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in…

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel…

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…

Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…

This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog"…

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.…

Recently, the task of image generation has attracted much attention. In particular, the recent empirical successes of the Markov Chain Monte Carlo (MCMC) technique of Langevin Dynamics have prompted a number of theoretical advances; despite…

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the…

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the…

Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from…

Stochastic sampling algorithms such as Langevin Monte Carlo are inspired by physical systems in a heat bath. Their equilibrium distribution is the canonical ensemble given by a prescribed target distribution, so they must balance…

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…

Cyclical MCMC is a novel MCMC framework recently proposed by Zhang et al. (2019) to address the challenge posed by high-dimensional multimodal posterior distributions like those arising in deep learning. The algorithm works by generating a…