SpreadNUTS -- Moderate Dynamic Extension of Paths for No-U-Turn Sampling & Partitioning Visited Regions

TL;DR

This paper proposes a modified version of the NUTS algorithm, called SpreadNUTS, which aims to explore the sample space more efficiently and achieve faster convergence than the original NUTS in Hamiltonian Monte Carlo methods.

Contribution

The paper introduces SpreadNUTS, a dynamic extension of NUTS, enhancing exploration speed and convergence in Hamiltonian Monte Carlo sampling.

Findings

SpreadNUTS explores sample space faster than NUTS.

SpreadNUTS achieves quicker convergence to the target distribution.

The method improves practical efficiency of HMC sampling.

Abstract

Markov chain Monte Carlo (MCMC) methods have existed for a long time and the field is well-explored. The purpose of MCMC methods is to approximate a distribution through repeated sampling; most MCMC algorithms exhibit asymptotically optimal behavior in that they converge to the true distribution at the limit. However, what differentiates these algorithms are their practical convergence guarantees and efficiency. While a sampler may eventually approximate a distribution well, because it is used in the real world it is necessary that the point at which the sampler yields a good estimate of the distribution is reachable in a reasonable amount of time. Similarly, if it is computationally difficult or intractable to produce good samples from a distribution for use in estimation, then there is no real-world utility afforded by the sampler. Thus, most MCMC methods these days focus on improving efficiency and speeding up convergence. However, many MCMC algorithms suffer from random walk behavior and often only mitigate such behavior as outright erasing random walks is difficult. Hamiltonian Monte Carlo (HMC) is a class of MCMC methods that theoretically exhibit no random walk behavior because of properties related to Hamiltonian dynamics. This paper introduces modifications to a specific HMC algorithm known as the no-U-turn sampler (NUTS) that aims to explore the sample space faster than NUTS, yielding a sampler that has faster convergence to the true distribution than NUTS.