Robust Covariance Adaptation in Adaptive Importance Sampling

TL;DR

This paper introduces a novel covariance adaptation scheme for adaptive importance sampling that prevents weight degeneracy and improves performance in high-dimensional problems.

Contribution

It proposes a new method leveraging recent IS advances to adapt covariance matrices effectively, addressing a key challenge in AIS.

Findings

Significant performance improvements in high-dimensional scenarios.

Effective prevention of weight degeneracy during adaptation.

Validated through comprehensive computer simulations.

Abstract

Importance sampling (IS) is a Monte Carlo methodology that allows for approximation of a target distribution using weighted samples generated from another proposal distribution. Adaptive importance sampling (AIS) implements an iterative version of IS which adapts the parameters of the proposal distribution in order to improve estimation of the target. While the adaptation of the location (mean) of the proposals has been largely studied, an important challenge of AIS relates to the difficulty of adapting the scale parameter (covariance matrix). In the case of weight degeneracy, adapting the covariance matrix using the empirical covariance results in a singular matrix, which leads to poor performance in subsequent iterations of the algorithm. In this paper, we propose a novel scheme which exploits recent advances in the IS literature to prevent the so-called weight degeneracy. The method efficiently adapts the covariance matrix of a population of proposal distributions and achieves a significant performance improvement in high-dimensional scenarios. We validate the new method through computer simulations.