NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport

TL;DR

NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport introduces a neural transport method with inverse autoregressive flows to improve sampling efficiency in complex posterior distributions, significantly outperforming standard HMC.

Contribution

The paper presents NeuTra HMC, a novel approach that learns a warping of the posterior geometry using neural flows to enhance Hamiltonian Monte Carlo sampling efficiency.

Findings

NeuTra HMC reduces convergence time compared to vanilla HMC.

NeuTra HMC achieves higher effective sample sizes in experiments.

The method effectively handles challenging posterior geometries.

Abstract

Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution and its gradient to converge and mix. We propose neural transport (NeuTra) HMC, a technique for learning to correct this sort of unfavorable geometry using inverse autoregressive flows (IAF), a powerful neural variational inference technique. The IAF is trained to minimize the KL divergence from an isotropic Gaussian to the warped posterior, and then HMC sampling is performed in the warped space. We evaluate NeuTra HMC on a variety of synthetic and real problems, and find that it significantly outperforms vanilla HMC both in time to reach the stationary distribution and asymptotic effective-sample-size rates.