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In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging…

Machine Learning · Statistics 2025-12-02 Tim Johnston , Iosif Lytras , Nikolaos Makras , Sotirios Sabanis

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 a class of interacting particle systems for implementing a maximum marginal likelihood estimation (MMLE) procedure to estimate the parameters of a latent variable model. We achieve this by formulating a continuous-time…

We address the problem of simulating efficiently from the posterior distribution over the parameters of a particular class of nonlinear regression models using a Langevin-Metropolis sampler. It is shown that as the number N of parameters…

Probability · Mathematics 2007-05-23 Laird Arnault Breyer , Mauro Piccioni , Sergio Scarlatti

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…

Computation · Statistics 2024-06-24 Vishwak Srinivasan , Andre Wibisono , Ashia Wilson

Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…

Numerical Analysis · Mathematics 2025-08-11 Tony Lelièvre , Régis Santet , Gabriel Stoltz

Standard first-order Langevin algorithms such as the unadjusted Langevin algorithm (ULA) are obtained by discretizing the Langevin diffusion and are widely used for sampling in machine learning because they scale to high dimensions and…

Machine Learning · Statistics 2025-09-25 Mert Gurbuzbalaban , Hoang M. Nguyen , Xicheng Zhang , Lingjiong Zhu

In this paper, we consider sampling from a class of distributions with thin tails supported on $\mathbb{R}^d$ and make two primary contributions. First, we propose a new Metropolized Algorithm With Optimization Step (MAO), which is well…

Machine Learning · Statistics 2021-12-02 EL Mahdi Khribch , George Deligiannidis , Daniel Paulin

Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as…

Medical Physics · Physics 2026-05-26 Moritz Blumenthal , Tina Holliber , Jonathan I. Tamir , Martin Uecker

In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…

Computation · Statistics 2015-10-12 Alexandros Beskos , Gareth Roberts , Alexandre Thiery , Natesh Pillai

This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin…

Statistics Theory · Mathematics 2015-09-14 Amandine Schreck , Gersende Fort , Sylvain Le Corff , Eric Moulines

Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…

Data Analysis, Statistics and Probability · Physics 2020-07-01 Zofia Trstanova , Ben Leimkuhler , Tony Lelièvre

Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler Maruyama discretization of the Langevin diffusion process, referred as Unadjusted Langevin Algorithm (ULA),…

Computation · Statistics 2021-07-28 Dao Nguyen , Xin Dang , Yixin Chen

The Random Walk Metropolis (RWM) algorithm is a Metropolis- Hastings MCMC algorithm designed to sample from a given target distribution \pi with Lebesgue density on R^N. RWM constructs a Markov chain by randomly proposing a new position…

Probability · Mathematics 2016-08-31 J. Kuntz , M. Ottobre , A. M. Stuart

We present an improved analysis of the Euler-Maruyama discretization of the Langevin diffusion. Our analysis does not require global contractivity, and yields polynomial dependence on the time horizon. Compared to existing approaches, we…

Probability · Mathematics 2019-11-05 Wenlong Mou , Nicolas Flammarion , Martin J. Wainwright , Peter L. Bartlett

We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$. We assume that the target density satisfies a log-Sobolev…

Machine Learning · Computer Science 2022-04-25 Khashayar Gatmiry , Santosh S. Vempala

In this work we study the diffusion annealed Langevin dynamics, a score-based diffusion process recently introduced in the theory of generative models and which is an alternative to the classical overdamped Langevin diffusion. Our goal is…

Probability · Mathematics 2025-11-14 Patrick Cattiaux , Paula Cordero-Encinar , Arnaud Guillin

In this paper, we propose irreversible versions of the Metropolis Hastings (MH) and Metropolis adjusted Langevin algorithm (MALA) with a main focus on the latter. For the former, we show how one can simply switch between different proposal…

Methodology · Statistics 2018-03-14 Yi-An Ma , Emily B. Fox , Tianqi Chen , Lei Wu

We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…

Machine Learning · Statistics 2023-10-03 Hong Ye Tan , Stanley Osher , Wuchen Li

Riemannian manifold Hamiltonian (RMHMC) and Lagrangian Monte Carlo (LMC) have emerged as powerful methods of Bayesian inference. Unlike Euclidean Hamiltonian Monte Carlo (EHMC) and the Metropolis-adjusted Langevin algorithm (MALA), the…

Methodology · Statistics 2023-01-05 James A. Brofos , Vivekananda Roy , Roy R. Lederman