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We present a nonlinear (in the sense of McKean) generalization of Hamiltonian Monte Carlo (HMC) termed nonlinear HMC (nHMC) capable of sampling from nonlinear probability measures of mean-field type. When the underlying confinement…

Probability · Mathematics 2023-09-22 Nawaf Bou-Rabee , Katharina Schuh

Hamiltonian Monte Carlo is a popular sampling technique for smooth target densities. The scale lengths of the target have long been known to influence integration error and sampling efficiency. However, quantitative measures intrinsic to…

Computation · Statistics 2020-02-06 Ian Langmore , Michael Dikovsky , Scott Geraedts , Peter Norgaard , Rob Von Behren

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is…

Machine Learning · Statistics 2020-09-02 Ziming Liu , Zheng Zhang

We study convergence rates of Hamiltonian Monte Carlo (HMC) algorithms with leapfrog integration under mild conditions on stochastic gradient oracle for the target distribution (SGHMC). Our method extends standard HMC by allowing the use of…

Statistics Theory · Mathematics 2024-05-28 Soumyadip Ghosh , Yingdong Lu , Tomasz Nowicki

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…

Computation · Statistics 2017-04-19 Cheng Zhang , Babak Shahbaba , Hongkai Zhao

Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…

Computation · Statistics 2026-04-07 Arghya Mukherjee , Dootika Vats

In Bayesian inference, Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm known for its efficiency in sampling from complex probability distributions. However, its application to models with latent…

Computation · Statistics 2025-04-15 Alaa Amri , Víctor Elvira , Amy L. Wilson

Hybrid Monte-Carlo (HMC) sampling smoother is a fully non-Gaussian four-dimensional data assimilation algorithm that works by directly sampling the posterior distribution formulated in the Bayesian framework. The smoother in its original…

Numerical Analysis · Computer Science 2016-12-21 Ahmed Attia , Razvan Stefanescu , Adrian Sandu

Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce high-quality Markov chain Monte Carlo-output even for very challenging target distributions. To this end, a symmetric positive definite scaling matrix for RMHMC,…

Computation · Statistics 2017-05-17 Tore Selland Kleppe

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art…

Computational Engineering, Finance, and Science · Computer Science 2024-05-09 Dhruv V. Patel , Jonghyun Lee , Matthew W. Farthing , Peter K. Kitanidis , Eric F. Darve

Hamiltonian Monte Carlo (HMC) has emerged as a powerful Markov Chain Monte Carlo (MCMC) method to sample from complex continuous distributions. However, a fundamental limitation of HMC is that it can not be applied to distributions with…

Computation · Statistics 2021-12-10 Guangyao Zhou

The efficiency of Hamiltonian Monte Carlo (HMC) can suffer when sampling a distribution with a wide range of length scales, because the small step sizes needed for stability in high-curvature regions are inefficient elsewhere. To address…

Machine Learning · Statistics 2023-11-09 Chirag Modi , Alex Barnett , Bob Carpenter

This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…

Probability · Mathematics 2024-05-14 Evan Camrud , Alain Durmus , Pierre Monmarché , Gabriel Stoltz

Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain…

Computation · Statistics 2020-06-22 Jonghyun Yun , Minsuk Shin , Ick Hoon Jin , Faming Liang

We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to…

Data Structures and Algorithms · Computer Science 2021-10-28 Yin Tat Lee , Ruoqi Shen , Kevin Tian

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method that allows to sample high dimensional probability measures. It relies on the integration of the Hamiltonian dynamics to propose a move which is then accepted or rejected…

Numerical Analysis · Mathematics 2023-08-08 Tony Lelièvre , Régis Santet , Gabriel Stoltz

The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…

Computation · Statistics 2025-01-27 Abraham Granados , Isaías Bañales

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Machine Learning · Statistics 2016-10-19 Wenbo Hu , Jun Zhu , Bo Zhang

We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm…

Computational Physics · Physics 2019-10-29 G. Margazoglou , L. Biferale , R. Grauer , K. Jansen , D. Mesterházy , T. Rosenow , R. Tripiccione

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) approach that exhibits favourable exploration properties in high-dimensional models such as neural networks. Unfortunately, HMC has limited use in large-data regimes and…

Machine Learning · Statistics 2020-10-15 Adam D. Cobb , Brian Jalaian