The Apogee to Apogee Path Sampler

TL;DR

The paper introduces the Apogee to Apogee Path Sampler (AAPS), a new MCMC method leveraging the invariance of local maxima in Hamiltonian paths to improve robustness and efficiency in sampling complex distributions.

Contribution

AAPS is a novel sampling algorithm that uses apogees invariance to enhance robustness and efficiency over traditional Hamiltonian Monte Carlo methods.

Findings

AAPS achieves similar efficiency to HMC.

AAPS is more robust to tuning parameter settings.

Empirical results demonstrate AAPS's effectiveness.

Abstract

Amongst Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the integration-time tuning parameter, $T$. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of local maxima in the potential along a path, or apogees, is the same whatever point (position and momentum) along the path is chosen to initialise the integration. We present the Apogee to Apogee Path Sampler (AAPS), which utilises this invariance to create a simple yet generic methodology for constructing a path, proposing a point from it and accepting or rejecting that proposal so as to target the intended distribution. We demonstrate empirically that AAPS has a similar efficiency to HMC but is much more robust to the setting of its equivalent tuning parameter, the number of apogees that the path crosses.