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Related papers: Adaptive stepsize algorithms for Langevin dynamics

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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…

Methodology · Statistics 2016-05-30 Christopher Nemeth , Chris Sherlock , Paul Fearnhead

In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant…

Probability · Mathematics 2019-10-07 Kaitong Hu , Anna Kazeykina , Zhenjie Ren

The kinetic Langevin dynamics finds diverse applications in various disciplines such as molecular dynamics and Hamiltonian Monte Carlo sampling. In this paper, a novel splitting scalar auxiliary variable (SSAV) scheme is proposed for the…

Numerical Analysis · Mathematics 2025-09-05 Lei Dai , Yingsong Jiang , Xiaojie Wang

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

Numerical Analysis · Mathematics 2012-04-10 Stéphane Descombes , Max Duarte , Thierry Dumont , Violaine Louvet , Marc Massot

In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…

Dynamical Systems · Mathematics 2014-08-04 Xavier Garcia , Jennifer Kunze , Thomas Rudelius , Anthony Sanchez , Sijing Shao , Emily Speranza , Chad Vidden

Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…

Statistics Theory · Mathematics 2026-02-18 Armand Gissler , Saeed Saremi , Francis Bach

In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…

Optimization and Control · Mathematics 2017-11-01 Raghu Bollapragada , Richard Byrd , Jorge Nocedal

We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…

Analysis of PDEs · Mathematics 2010-08-23 Chris Chipot , Tony Lelièvre

We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the…

Machine Learning · Statistics 2020-03-04 Jing An , Jianfeng Lu , Lexing Ying

Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…

Machine Learning · Statistics 2022-11-04 Jacopo Guidolin , Vyacheslav Kungurtsev , Ondřej Kuželka

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into…

Biological Physics · Physics 2026-04-17 David B. Brückner , Pierre Ronceray , Chase P. Broedersz

Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…

Computation · Statistics 2020-06-02 Valentin De Bortoli , Alain Durmus , Marcelo Pereyra , Ana F. Vidal

The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…

Machine Learning · Computer Science 2022-11-22 Yuri Kinoshita , Taiji Suzuki

Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal…

Optimization and Control · Mathematics 2023-10-05 Enric Ribera Borrell , Jannes Quer , Lorenz Richter , Christof Schütte

Current molecular dynamic simulations of biomolecules using multiple time steps to update the slowingly changing force are hampered by an instability occuring at time step equal to half the period of the fastest vibrating mode. This has…

Chemical Physics · Physics 2009-11-10 Siu A. Chin

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

We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in…

Optimization and Control · Mathematics 2018-06-08 Andre Wibisono

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…

Machine Learning · Computer Science 2024-09-18 Mohammad Reza Karimi , Ya-Ping Hsieh , Andreas Krause

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

Bayesian neural networks (BNNs) require scalable sampling algorithms to approximate posterior distributions over parameters. Existing stochastic gradient Markov Chain Monte Carlo (SGMCMC) methods are highly sensitive to the choice of…

Machine Learning · Computer Science 2026-04-10 Rajit Rajpal , Benedict Leimkuhler , Yuanhao Jiang