General-purpose post-sampling reweighting method for multimodal target measures

TL;DR

This paper introduces a reweighting method for accurately estimating probabilities in multi-modal distributions, addressing the challenge of correctly representing each mode after sampling.

Contribution

It proposes a simple reweighting scheme based on minimizing the KL divergence to improve probability estimates in multi-modal sampling scenarios.

Findings

Effective in correctly estimating mode probabilities

Applicable to locally sampled multi-modal distributions

Improves accuracy over naive sampling methods

Abstract

When sampling multi-modal probability distributions, correctly estimating the relative probability of each mode, even when the modes have been discovered and locally sampled, remains challenging. We test a simple reweighting scheme designed for this situation, which consists in minimizing (in terms of weights) the Kullback-Leibler divergence of a weighted (regularized) empirical distribution of the samples with respect to the target measure.