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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

Langevin MCMC gradient optimization is a class of increasingly popular methods for estimating a posterior distribution. This paper addresses the algorithm as applied in a decentralized setting, wherein data is distributed across a network…

Optimization and Control · Mathematics 2020-09-22 Vyacheslav Kungurtsev

We develop a discrete optimal transport framework for analyzing simulated annealing algorithms on finite state spaces. Building on the discrete Wasserstein metric introduced by Maas (J. Funct. Anal., 2011), we define a generalized discrete…

Data Structures and Algorithms · Computer Science 2026-05-08 Yuchen He , Tianhui Jiang , Sihan Wang , Chihao Zhang

We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically…

Machine Learning · Statistics 2026-05-18 Hong Ye Tan , Stanley Osher , Wuchen Li

We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles, we consider a second-order score-based ODE, similar to…

Machine Learning · Statistics 2026-01-19 Hong Ye Tan , Stanley Osher , Wuchen Li

We study the problem of sampling from a distribution $p^*(x) \propto \exp\left(-U(x)\right)$, where the function $U$ is $L$-smooth everywhere and $m$-strongly convex outside a ball of radius $R$, but potentially nonconvex inside this ball.…

When sampling multi-modal probability distributions, correctly estimating the relative probability of each mode, even when the modes have been discovered and locally sampled, remains challenging. We test a simple reweighting scheme designed…

Statistics Theory · Mathematics 2026-02-17 Pierre Monmarché

Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…

Computation · Statistics 2025-10-24 Adrien Vacher , Omar Chehab , Anna Korba

We study the problem of sampling from a probability distribution on $\mathbb R^p$ defined via a convex and smooth potential function. We consider a continuous-time diffusion-type process, termed Penalized Langevin dynamics (PLD), the drift…

Statistics Theory · Mathematics 2020-06-26 Avetik Karagulyan , Arnak S. Dalalyan

Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where…

Machine Learning · Computer Science 2025-03-18 Qingshi Sun , Nathan Justin , Andres Gomez , Phebe Vayanos

A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…

Computation · Statistics 2023-11-01 Martin Chak , Nikolas Kantas , Tony Lelièvre , Grigorios A. Pavliotis

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC),…

Machine Learning · Statistics 2026-04-07 Yingli Wang , Changwei Tu , Xiaoyu Wang , Lingjiong Zhu

We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte…

Machine Learning · Statistics 2024-05-30 Tim Tsz-Kit Lau , Han Liu , Thomas Pock

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…

Statistical Mechanics · Physics 2015-09-30 M. Ohzeki , A. Ichiki

Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable posterior sampling and decentralized variants enabling…

Optimization and Control · Mathematics 2025-11-18 Waheed U. Bajwa , Mert Gurbuzbalaban , Mustafa Ali Kutbay , Lingjiong Zhu , Muhammad Zulqarnain

We study the problem of sampling from a target distribution $\pi(q)\propto e^{-U(q)}$ on $\mathbb{R}^d$, where $U$ can be non-convex, via the Hessian-free high-resolution (HFHR) dynamics, which is a second-order Langevin-type process that…

Probability · Mathematics 2026-01-07 Xiaoyu Wang , Yingli Wang , Lingjiong Zhu

Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples…

Machine Learning · Statistics 2021-10-11 Zheyang Shen , Markus Heinonen , Samuel Kaski

It is well known that adding any skew symmetric matrix to the gradient of Langevin dynamics algorithm results in a non-reversible diffusion with improved convergence rate. This paper presents a gradient algorithm to adaptively optimize the…

Machine Learning · Computer Science 2020-09-29 Vikram Krishnamurthy , George Yin

A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap…

Machine Learning · Computer Science 2018-10-23 Will Grathwohl , Ricky T. Q. Chen , Jesse Bettencourt , Ilya Sutskever , David Duvenaud

This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…

Machine Learning · Statistics 2026-05-05 Yiye Jiang , Jérémie Bigot