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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

We provide a clarification of the description of Langevin diffusions on Riemannian manifolds and of the measure underlying the invariant density. As a result we propose a new position-dependent Metropolis-adjusted Langevin algorithm (MALA)…

Methodology · Statistics 2014-08-15 Tatiana Xifara , Chris Sherlock , Samuel Livingstone , Simon Byrne , Mark Girolami

We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with log-concave and smooth densities. The higher-order dynamics allow for more flexible discretization schemes,…

Machine Learning · Statistics 2020-05-27 Wenlong Mou , Yi-An Ma , Martin J. Wainwright , Peter L. Bartlett , Michael I. Jordan

Preconditioning is a common method applied to modify Markov chain Monte Carlo algorithms with the goal of making them more efficient. In practice it is often extremely effective, even when the preconditioner is learned from the chain. We…

Computation · Statistics 2026-02-12 Max Hird , Florian Maire , Jeffrey Negrea

Sampling from constrained statistical distributions is a fundamental task in various fields including Bayesian statistics, computational chemistry, and statistical physics. This article considers the cases where the constrained distribution…

Machine Learning · Computer Science 2025-10-28 Kijung Jeon , Michael Muehlebach , Molei Tao

The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm that incorporates the gradient of the logarithm of the target density in its proposal distribution. In an earlier joint work \citet{pill:stu:12}, the author had…

Computation · Statistics 2025-01-15 Natesh S. Pillai

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…

Machine Learning · Statistics 2024-10-22 Jason M. Altschuler , Kunal Talwar

We present a new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of deep learning models. Its underpinning theory relies on recent…

Machine Learning · Computer Science 2024-03-05 Dong-Young Lim , Sotirios Sabanis

We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves $\varepsilon$ error (in 2-Wasserstein…

Machine Learning · Statistics 2018-01-30 Xiang Cheng , Niladri S. Chatterji , Peter L. Bartlett , Michael I. Jordan

In this paper, we consider the underdamped Langevin diffusion (ULD) and propose a numerical approximation using its associated ordinary differential equation (ODE). When used as a Markov Chain Monte Carlo (MCMC) algorithm, we show that the…

Numerical Analysis · Mathematics 2021-01-26 James Foster , Terry Lyons , Harald Oberhauser

Langevin dynamics (LD) has been proven to be a powerful technique for optimizing a non-convex objective as an efficient algorithm to find local minima while eventually visiting a global minimum on longer time-scales. LD is based on the…

Optimization and Control · Mathematics 2020-10-06 Xuefeng Gao , Mert Gurbuzbalaban , Lingjiong Zhu

We propose a federated averaging Langevin algorithm (FA-LD) for uncertainty quantification and mean predictions with distributed clients. In particular, we generalize beyond normal posterior distributions and consider a general class of…

Machine Learning · Statistics 2023-10-06 Wei Deng , Qian Zhang , Yi-An Ma , Zhao Song , Guang Lin

Langevin Dynamics has been extensively employed in global non-convex optimization due to the concentration of its stationary distribution around the global minimum of the potential function at low temperatures. In this paper, we propose to…

Optimization and Control · Mathematics 2023-05-22 Ryo Fujino

Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a…

Machine Learning · Statistics 2020-07-07 Yi Chen , Jinglin Chen , Jing Dong , Jian Peng , Zhaoran Wang

Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…

Machine Learning · Computer Science 2025-10-10 Saravanan Kandasamy , Dheeraj Nagaraj

We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov…

Computation · Statistics 2025-05-30 Paula Cordero Encinar , Francesca R. Crucinio , O. Deniz Akyildiz

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…

Machine Learning · Statistics 2020-06-17 Adil Salim , Dmitry Kovalev , Peter Richtárik

Sampling from heavy-tailed and multimodal distributions is challenging when neither the target density nor the proposal density can be evaluated, as in $\alpha$-stable L\'evy-driven fractional Langevin algorithms. While the target…

Machine Learning · Statistics 2026-02-03 Ahmed Aloui , Junyi Liao , Ali Hasan , Jose Blanchet , Vahid Tarokh

The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension…

Machine Learning · Statistics 2025-09-05 Yifan Chen , Xiaoou Cheng , Jonathan Niles-Weed , Jonathan Weare

We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential…

Machine Learning · Computer Science 2025-04-16 Hengrong Du , Qi Feng , Changwei Tu , Xiaoyu Wang , Lingjiong Zhu