Relative Entropy Gradient Sampler for Unnormalized Distributions

TL;DR

The paper introduces REGS, a particle-based sampling method leveraging Wasserstein gradient flow and neural network-based density ratio estimation to efficiently sample from unnormalized, complex distributions, outperforming existing methods.

Contribution

It presents a novel particle sampling algorithm using Wasserstein gradient flow and neural networks for density ratio estimation, improving sampling from unnormalized distributions.

Findings

REGS outperforms state-of-the-art sampling methods in simulations.

Effective in challenging multimodal distributions.

Demonstrates superior performance in Bayesian logistic regression.

Abstract

We propose a relative entropy gradient sampler (REGS) for sampling from unnormalized distributions. REGS is a particle method that seeks a sequence of simple nonlinear transforms iteratively pushing the initial samples from a reference distribution into the samples from an unnormalized target distribution. To determine the nonlinear transforms at each iteration, we consider the Wasserstein gradient flow of relative entropy. This gradient flow determines a path of probability distributions that interpolates the reference distribution and the target distribution. It is characterized by an ODE system with velocity fields depending on the density ratios of the density of evolving particles and the unnormalized target density. To sample with REGS, we need to estimate the density ratios and simulate the ODE system with particle evolution. We propose a novel nonparametric approach to estimating the logarithmic density ratio using neural networks. Extensive simulation studies on challenging multimodal 1D and 2D mixture distributions and Bayesian logistic regression on real datasets demonstrate that the REGS outperforms the state-of-the-art sampling methods included in the comparison.