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Related papers: Non-asymptotic mixing of the MALA algorithm

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We analyse computational efficiency of Metropolis-Hastings algorithms with stochastic AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g.…

Computation · Statistics 2016-05-23 Richard A. Norton , Colin Fox

In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…

Statistics Theory · Mathematics 2017-07-28 Ajay Jasra , Kengo Kamatani , Hiroki Masuda

Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. However, locally Lipschitz SDEs often require special…

Numerical Analysis · Mathematics 2021-02-26 Xingjie Li , Fei Lu , Felix X. -F. Ye

Out of the recent advances in systems and control (S\&C)-based analysis of optimization algorithms, not enough work has been specifically dedicated to machine learning (ML) algorithms and its applications. This paper addresses this gap by…

Machine Learning · Computer Science 2021-02-15 Orlando Romero , Subhro Das , Pin-Yu Chen , Sérgio Pequito

We present an unbiased method for Bayesian posterior means based on kinetic Langevin dynamics that combines advanced splitting methods with enhanced gradient approximations. Our approach avoids Metropolis correction by coupling Markov…

Computation · Statistics 2025-12-04 Neil K. Chada , Benedict Leimkuhler , Daniel Paulin , Peter A. Whalley

Obtaining coarse-grained models that accurately incorporate finite-size effects is an important open challenge in the study of complex, multi-scale systems. We apply Langevin regression, a recently developed method for finding stochastic…

Adaptation and Self-Organizing Systems · Physics 2021-10-12 Jordan Snyder , Jared L. Callaham , Steven L. Brunton , J. Nathan Kutz

This paper investigates the stochastic Cahn-Hilliard equation (SCHE) driven by additive space-time white noise. We first refine the analytical ergodic theory by proving that the continuum equation admits a unique invariant measure in the…

Numerical Analysis · Mathematics 2025-12-09 Nan Deng , Yibo Wang , Wanrong Cao

We propose a reflection-free Langevin framework for sampling and optimization on compact polyhedra. The method is based on the inverse Hessian of the logarithmic barrier, which defines a Dikin--Langevin diffusion whose drift and noise adapt…

Computation · Statistics 2026-03-17 James Chok , Domenic Petzinna

We present a novel multilevel Monte Carlo approach for estimating quantities of interest for stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and Szpruch: Antithetic multilevel Monte Carlo estimation for…

Numerical Analysis · Mathematics 2025-04-15 Abdul-Lateef Haji-Ali , Andreas Stein

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is…

Numerical Analysis · Mathematics 2020-08-20 Guoting Song , Junhao Hu , Shuaibin Gao , Xiaoyue Li

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 tuning of stochastic gradient algorithms (SGAs) for optimization and sampling is often based on heuristics and trial-and-error rather than generalizable theory. We address this theory--practice gap by characterizing the large-sample…

Computation · Statistics 2023-07-21 Jeffrey Negrea , Jun Yang , Haoyue Feng , Daniel M. Roy , Jonathan H. Huggins

Motivated by problems arising in decentralized control problems and non-cooperative Nash games, we consider a class of strongly monotone Cartesian variational inequality (VI) problems, where the mappings either contain expectations or their…

Optimization and Control · Mathematics 2013-01-10 Farzad Yousefian , Angelia Nedić , Uday V. Shanbhag

This paper studies explicit numerical approximations of the invariant probability measures (IPMs) for stochastic functional differential equations (SFDEs) with infinite delay under one-sided Lipschitz condition on the drift coefficient. To…

Numerical Analysis · Mathematics 2026-03-06 Guozhen Li , Shan Huang , Xiaoyue Li , Xuerong Mao

A fundamental problem in modern supervised learning is computing reliable conditional prediction intervals in high-dimensional settings: existing methods often rely on restrictive modelling assumptions, do not scale as predictor dimension…

Machine Learning · Statistics 2026-02-24 Daniel Salnikov , Dan Leonte , Kevin Michalewicz

In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…

Computation · Statistics 2020-10-19 Yanxin Li , Stephen G. Walker

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem in three ways: it generates…

Methodology · Statistics 2015-09-22 Sebastian J. Vollmer , Konstantinos C. Zygalakis , and Yee Whye Teh

We present a novel universal gradient method for solving convex optimization problems. Our algorithm, Dual Averaging with Distance Adaptation (DADA), is based on the classical scheme of dual averaging and dynamically adjusts its…

Optimization and Control · Mathematics 2026-04-22 Mohammad Moshtaghifar , Anton Rodomanov , Daniil Vankov , Sebastian Stich

We study the Multiple-try Metropolis algorithm using the framework of Poincar\'e inequalities. We describe the Multiple-try Metropolis as an auxiliary variable implementation of a resampling approximation to an ideal Metropolis--Hastings…

Computation · Statistics 2025-11-18 Rocco Caprio , Sam Power , Andi Q. Wang

We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…

Systems and Control · Electrical Eng. & Systems 2020-11-30 Zheming Wang , Raphaël M. Jungers , Chong-Jin Ong