Related papers: Using Perturbed Underdamped Langevin Dynamics to E…

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…

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and…

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 Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains.…

We propose an adaptively weighted stochastic gradient Langevin dynamics algorithm (SGLD), so-called contour stochastic gradient Langevin dynamics (CSGLD), for Bayesian learning in big data statistics. The proposed algorithm is essentially a…

Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too…

We propose and analyze a class of adaptive sampling algorithms for multimodal distributions on a bounded domain, which share a structural resemblance to the classic overdamped Langevin dynamics. We first demonstrate that this class of…

Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients…

A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…

In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler…

Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin…

We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced…

The scaling of the mobility of two-dimensional Langevin dynamics in a periodic potential as the friction vanishes is not well understood for non-separable potentials. Theoretical results are lacking, and numerical calculation of the…

Sampling from high-dimensional distributions has wide applications in data science and machine learning but poses significant computational challenges. We introduce Subspace Langevin Monte Carlo (SLMC), a novel and efficient sampling method…

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…

We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…