Rare Events via Cross-Entropy Population Monte Carlo

TL;DR

This paper introduces a novel Cross-Entropy population Monte Carlo algorithm that optimizes distributions individually with deterministic weights, outperforming existing methods especially in high-dimensional scenarios.

Contribution

The method departs from traditional mixture optimization by using deterministic weights and reinterpreting the cross-entropy derivation, improving performance in complex problems.

Findings

Outperforms existing resampling population Monte Carlo methods

Effective in higher-dimensional problems

Demonstrated through numerical examples

Abstract

We present a Cross-Entropy based population Monte Carlo algorithm. This methods stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the distributions individually through a reinterpretation of the typical derivation of the cross-entropy method. Demonstrations on numerical examples show that the algorithm can outperform existing resampling population Monte Carlo methods, especially for higher-dimensional problems.