English
Related papers

Related papers: Riemannian Manifold Hamiltonian Monte Carlo

200 papers

The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…

Machine Learning · Computer Science 2019-06-04 Minghao Gu , Shiliang Sun

Hamiltonian Monte Carlo (HMC) is a Markov chain algorithm for sampling from a high-dimensional distribution with density $e^{-f(x)}$, given access to the gradient of $f$. A particular case of interest is that of a $d$-dimensional Gaussian…

Machine Learning · Statistics 2022-09-27 Simon Apers , Sander Gribling , Dániel Szilágyi

In this work we present a new and efficient Bayesian method for nonlinear three dimensional large scale structure inference. We employ a Hamiltonian Monte Carlo (HMC) sampler to obtain samples from a multivariate highly non-Gaussian…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-14 J. Jasche , F. S. Kitaura

Standard Markov chain Monte Carlo methods struggle to explore distributions that are concentrated in the neighbourhood of low-dimensional structures. These pathologies naturally occur in a number of situations. For example, they are common…

Computation · Statistics 2021-12-02 Khai Xiang Au , Matthew M. Graham , Alexandre H. Thiery

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…

Computation · Statistics 2019-05-03 Khue-Dung Dang , Matias Quiroz , Robert Kohn , Minh-Ngoc Tran , Mattias Villani

We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization…

Machine Learning · Statistics 2019-01-24 Viktor Yanush , Dmitry Kropotov

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

The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…

Computation · Statistics 2019-04-22 Alessandro Barp , Anthony Kennedy , Mark Girolami

Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…

Methodology · Statistics 2015-02-02 Lotfi Chaari , Jean-Yves Tourneret , Caroline Chaux , Hadj Batatia

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

There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian…

Computation · Statistics 2021-06-08 Zexi Song , Zhiqiang Tan

Hamiltonian Monte Carlo (HMC) has been widely adopted in the statistics community because of its ability to sample high-dimensional distributions much more efficiently than other Metropolis-based methods. Despite this, HMC often performs…

Computation · Statistics 2019-11-19 Arya A. Pourzanjani , Linda R. Petzold

Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the Metropolis algorithm by reducing its random walk behavior. Riemannian Manifold HMC (RMHMC) further improves HMC's performance by exploiting the geometric properties…

Computation · Statistics 2015-06-22 Shiwei Lan , Vassilios Stathopoulos , Babak Shahbaba , Mark Girolami

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural…

Data Structures and Algorithms · Computer Science 2017-10-18 Yin Tat Lee , Santosh S. Vempala

We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to…

Machine Learning · Statistics 2019-10-15 Adam D. Cobb , Atılım Güneş Baydin , Andrew Markham , Stephen J. Roberts

Hamiltonian Monte Carlo (HMC) is widely used for sampling from high dimensional target distributions with densities known up to proportionality. While HMC exhibits favorable scaling properties in high dimensions, it struggles with strongly…

Computation · Statistics 2025-07-30 Joonha Park

In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to…

Computation · Statistics 2015-06-22 Shiwei Lan , Jeffrey Streets , Babak Shahbaba

Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…

Computation · Statistics 2025-04-28 Jimmy Huy Tran , Tore Selland Kleppe

We propose a variant of Hamiltonian Monte Carlo (HMC), called the Repelling-Attracting Hamiltonian Monte Carlo (RAHMC), for sampling from multimodal distributions. The key idea that underpins RAHMC is a departure from the conservative…

Statistics Theory · Mathematics 2024-03-08 Siddharth Vishwanath , Hyungsuk Tak

Markov Chain Monte Carlo (MCMC) is an invaluable means of inference with complicated models, and Hamiltonian Monte Carlo, in particular Riemannian Manifold Hamiltonian Monte Carlo (RMHMC), has demonstrated impressive success in many…

Methodology · Statistics 2015-03-02 M. J. Betancourt