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Related papers: Black-box unadjusted Hamiltonian Monte Carlo

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We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization…

Probability · Mathematics 2023-07-06 Nawaf Bou-Rabee , Katharina Schuh

Inexact Markov Chain Monte Carlo methods rely on Markov chains that do not exactly preserve the target distribution. Examples include the unadjusted Langevin algorithm (ULA) and unadjusted Hamiltonian Monte Carlo (uHMC). This paper…

Probability · Mathematics 2023-04-13 Alain Oliviero Durmus , Andreas Eberle

Sampling occupies an important position in theories of various scientific fields, and Markov chain Monte Carlo (MCMC) provides the most common technique of sampling. In the progress of MCMC, a huge number of studies have aimed the…

Statistical Mechanics · Physics 2021-07-20 Akihisa Ichiki , Masayuki Ohzeki

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

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters, based on…

Computational Physics · Physics 2025-12-10 Henrik Christiansen , Federico Errica , Francesco Alesiani

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

Computational Physics · Physics 2015-06-18 Youhan Fang , Jesus-Maria Sanz-Serna , Robert D. Skeel

Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time…

Machine Learning · Statistics 2016-09-15 Xiaoyu Lu , Valerio Perrone , Leonard Hasenclever , Yee Whye Teh , Sebastian J. Vollmer

The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities. Favorable scaling with dimension has led to wide adoption of HMC by the statistics community. Modern auto-differentiating software should allow more…

Computation · Statistics 2022-08-17 Ian Langmore , Michael Dikovsky , Scott Geraedts , Peter Norgaard , Rob von Behren

Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as a computationally fast and easily implemented method for performing full Bayesian analysis in hierarchical statistical models. The method relies on introducing a modified…

Computation · Statistics 2018-10-23 Tore Selland Kleppe

Recent studies on diffusion-based sampling methods have shown that Langevin Monte Carlo (LMC) algorithms can be beneficial for non-convex optimization, and rigorous theoretical guarantees have been proven for both asymptotic and finite-time…

Optimization and Control · Mathematics 2019-01-23 Thanh Huy Nguyen , Umut Şimşekli , Gaël Richard

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

We present a new Subset Simulation approach using Hamiltonian neural network-based Monte Carlo sampling for reliability analysis. The proposed strategy combines the superior sampling of the Hamiltonian Monte Carlo method with…

Machine Learning · Statistics 2024-01-11 Denny Thaler , Somayajulu L. N. Dhulipala , Franz Bamer , Bernd Markert , Michael D. Shields

We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte…

Machine Learning · Statistics 2024-05-30 Tim Tsz-Kit Lau , Han Liu , Thomas Pock

Tuning the durations of the Hamiltonian flow in Hamiltonian Monte Carlo (also called Hybrid Monte Carlo) (HMC) involves a tradeoff between computational cost and sampling quality, which is typically challenging to resolve in a satisfactory…

Probability · Mathematics 2017-09-08 Nawaf Bou-Rabee , Jesus Maria Sanz-Serna

Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…

Statistical Mechanics · Physics 2026-04-20 Christoph Schönle , Davide Carbone , Marylou Gabrié , Tony Lelièvre , Gabriel Stoltz

Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…

Statistical Mechanics · Physics 2014-05-27 Jerome P. Nilmeier , Gavin E. Crooks , David D. L. Minh , John D. Chodera

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

Computation · Statistics 2019-04-29 Lingge Li , Andrew Holbrook , Babak Shahbaba , Pierre Baldi

Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…

High Energy Physics - Lattice · Physics 2023-07-31 Guilherme Catumba , Alberto Ramos , Bryan Zaldivar

Proposals for Metropolis-Hastings MCMC derived by discretizing Langevin diffusion or Hamiltonian dynamics are examples of stochastic autoregressive proposals that form a natural wider class of proposals with equivalent computability. We…

Computation · Statistics 2016-10-05 Richard A. Norton , Colin Fox

This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…

Numerical Analysis · Mathematics 2023-11-07 Ben Adcock , Simone Brugiapaglia