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In this paper, we investigate a continuous time version of the Stochastic Langevin Monte Carlo method, introduced in [WT11], that incorporates a stochastic sampling step inside the traditional over-damped Langevin diffusion. This method is…

Machine Learning · Statistics 2023-01-10 Marelys Crespo Navas , Sébastien Gadat , Xavier Gendre

We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from…

Computation · Statistics 2025-12-30 Nicolas Zilberstein , Santiago Segarra , Luiz Chamon

It is of significant interest in many applications to sample from a high-dimensional target distribution $\pi$ with the density $\pi(\text{d} x) \propto e^{-U(x)} (\text{d} x) $, based on the temporal discretization of the Langevin…

Numerical Analysis · Mathematics 2025-01-30 Chenxu Pang , Xiaojie Wang , Yue Wu

We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an…

Machine Learning · Computer Science 2021-02-24 Difan Zou , Pan Xu , Quanquan Gu

Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…

Computation · Statistics 2024-04-01 Riddhiman Bhattacharya , Tiefeng Jiang

Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning.…

Statistics Theory · Mathematics 2026-05-11 Bin Yang , Xiaojie Wang

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…

Computation · Statistics 2016-07-04 Thomas Bonis

The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…

Machine Learning · Statistics 2025-03-07 Zhiyan Ding , Qin Li

Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…

Statistics Theory · Mathematics 2022-11-01 Jason M. Altschuler , Kunal Talwar

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin…

Machine Learning · Statistics 2019-10-23 Yi-An Ma , Niladri Chatterji , Xiang Cheng , Nicolas Flammarion , Peter Bartlett , Michael I. Jordan

An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…

Machine Learning · Statistics 2025-09-09 Junhua Chen , Lorenz Richter , Julius Berner , Denis Blessing , Gerhard Neumann , Anima Anandkumar

We consider the outstanding problem of sampling from an unnormalized density that may be non-log-concave and multimodal. To enhance the performance of simple Markov chain Monte Carlo (MCMC) methods, techniques of annealing type have been…

Machine Learning · Statistics 2025-02-18 Wei Guo , Molei Tao , Yongxin Chen

Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…

Methodology · Statistics 2019-09-19 Charles Matthews , Jonathan Weare

Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have…

Data Structures and Algorithms · Computer Science 2018-12-18 Yin Tat Lee , Zhao Song , Santosh S. Vempala

We study sampling from a target distribution $\nu_* = e^{-f}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm when the potential $f$ satisfies a strong dissipativity condition and it is first-order smooth with a Lipschitz…

Machine Learning · Statistics 2021-07-09 Murat A. Erdogdu , Rasa Hosseinzadeh , Matthew S. Zhang

In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the Langevin Monte Carlo (LMC) algorithm, the Euler…

Statistics Theory · Mathematics 2021-12-07 Arnak S. Dalalyan , Avetik Karagulyan , Lionel Riou-Durand

Along with the recent advances in scalable Markov Chain Monte Carlo methods, sampling techniques that are based on Langevin diffusions have started receiving increasing attention. These so called Langevin Monte Carlo (LMC) methods are based…

Computation · Statistics 2017-06-14 Umut Şimşekli

In this paper, we study the problem of sampling from log-concave distributions supported on convex, compact sets, with a particular focus on the randomized midpoint discretization of both vanilla and kinetic Langevin diffusions in this…

Machine Learning · Statistics 2025-05-27 Yifeng Yu , Lu Yu

In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the…

Statistics Theory · Mathematics 2017-07-31 Arnak S. Dalalyan

We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each…

Statistics Theory · Mathematics 2026-01-13 Ruiyu Han , Gautam Iyer , Dejan Slepčev