Hybrid Monte Carlo with Chaotic Mixing

TL;DR

This paper introduces a hybrid Monte Carlo method leveraging chaotic trajectories for efficient sampling of high-dimensional distributions, showing faster autocorrelation decay and improved covariance estimation over traditional methods.

Contribution

It presents a novel HMC technique that utilizes chaotic mixing, reducing dependence on step-size tuning and enhancing sampling efficiency in complex distributions.

Findings

Faster decay of sample autocorrelations compared to traditional HMC

Produces superior covariance estimates in tested distributions

Effective even with sparse or no momentum re-sampling

Abstract

We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum distribution, and due to its mixing properties, exhibits sample-to-sample autocorrelations that decay far faster than those in the traditional hybrid Monte Carlo algorithm. We test the methods on distributions of varying correlation structure, finding that the proposed technique produces superior covariance estimates, is less reliant on step-size tuning, and can even function with sparse or no momentum re-sampling. The method presented here is promising for more general distributions, such as those that arise in Bayesian learning of artificial neural networks and in the state and parameter estimation of dynamical systems.