An Introduction to Hamiltonian Monte Carlo Method for Sampling

Abstract

The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $\pi (x)\propto e^{-f(x)}$. We focus on the "idealized" case, where one can compute continuous trajectories exactly. We show that idealized HMC preserves $\pi$ and we establish its convergence when $f$ is strongly convex and smooth.

arXiv commentThis exposition is to supplement the talk by the author at the Bootcamp in the semester on Geometric Methods for Optimization and Sampling at the Simons Institute for the Theory of Computing

References in corpus (8)

• Stochastic Gradient Hamiltonian Monte Carlo
• Diffusion limits of the random walk Metropolis algorithm in high dimensions
• Randomized Hamiltonian Monte Carlo
• Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm
• Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions
• Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions
• Optimizing The Integrator Step Size for Hamiltonian Monte Carlo
• On the convergence of Hamiltonian Monte Carlo