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We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin…

Statistical Mechanics · Physics 2008-08-22 Cristian Micheletti , Giovanni Bussi , Alessandro Laio

In this paper, we study the optimal filtering problem for a interacting particle system generated by stochastic differential equations with interaction. By using Malliavin calculus, we construct the differential equation of the covariance…

Optimization and Control · Mathematics 2024-09-04 Andrey Dorogovtsev , Yuecai Han , Kateryna Hlyniana , Yuhang Li

Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to apply corrector steps based on the unadjusted Langevin…

Machine Learning · Statistics 2026-05-12 Kevin H. Lam , Tyler Farghly , Christopher Williams , Jun Yang , Yee Whye Teh , Arnaud Doucet

We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…

Optimization and Control · Mathematics 2024-11-06 Martin Burger , Matthias J. Ehrhardt , Lorenz Kuger , Lukas Weigand

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…

Machine Learning · Statistics 2019-11-05 Song Liu , Takafumi Kanamori , Wittawat Jitkrittum , Yu Chen

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

Variance reduction methods are often needed for the reliability assessment of complex industrial systems, we focus on one variance reduction method in a given context, that is the interacting particle system method (IPS) used on piecewise…

Computation · Statistics 2019-07-24 H. Chraibi , A. Dutfoy , T. Galtier , J. Garnier

(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…

Computation · Statistics 2023-02-21 Juan Kuntz , Jen Ning Lim , Adam M. Johansen

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…

Statistics Theory · Mathematics 2012-03-12 Jinyuan Chang , Song Xi Chen

The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…

Probability · Mathematics 2019-10-21 Charles-Edouard Bréhier , Ludovic Goudenège , Loic Tudela

As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develop a deterministic particle method for the weighted porous medium equation (WPME) and prove its convergence on bounded time intervals. This…

Analysis of PDEs · Mathematics 2023-01-26 Katy Craig , Karthik Elamvazhuthi , Matt Haberland , Olga Turanova

The Metropolis-Adjusted Langevin Algorithm (MALA) is a Markov Chain Monte Carlo method which creates a Markov chain reversible with respect to a given target distribution, pi^N, with Lebesgue density on R^N; it can hence be used to…

Probability · Mathematics 2017-08-24 J. Kuntz , M. Ottobre , A. M. Stuart

We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…

Computation · Statistics 2021-09-27 Andrew Golightly , Chris Sherlock

This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…

Statistics Theory · Mathematics 2024-02-23 Denis Belomestny , Mark Podolskij , Shi-Yuan Zhou

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…

Statistics Theory · Mathematics 2010-08-18 Jimmy Olsson , Jonas Ströjby

We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…

Numerical Analysis · Mathematics 2024-01-30 Grigorios A. Pavliotis , Andrea Zanoni

The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…

Computation · Statistics 2016-11-07 Aliaksandr Hubin , Geir Storvik

Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables…

Statistical Mechanics · Physics 2022-11-22 Antonio Russo , Miguel A. Duran-Olivencia , Ioannis G. Kevrekidis , Serafim Kalliadasis

This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in…

Methodology · Statistics 2015-04-06 Marcelo Pereyra

Several important learning tasks can be formulated as minimizing an entropy-regularized objective over an appropriate space of probability distributions. Mean-field Langevin dynamics (MFLD) facilitate computation in this general context,…

Machine Learning · Computer Science 2026-05-28 Zonghao Chen , Heishiro Kanagawa , François-Xavier Briol , Chris J. Oates , Lester Mackey