Adaptive Importance Sampling in General Mixture Classes

TL;DR

This paper introduces an adaptive importance sampling algorithm that optimizes mixture densities by iteratively updating weights and parameters, improving sampling efficiency across various distributions.

Contribution

It presents a novel adaptive scheme for mixture importance sampling that includes a Rao-Blackwellisation technique to enhance performance.

Findings

Effective in artificial and real examples

Applicable to mixtures of multivariate Student t distributions

Improved sampling efficiency through adaptive updates

Abstract

In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the importance sampling performances, as measured by an entropy criterion. The method is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student t distributions. The performances of the proposed scheme are studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.