Optimality in Noisy Importance Sampling

TL;DR

This paper analyzes noisy importance sampling, deriving optimal proposal densities that account for noise variance, and compares these with previous approaches to improve estimation accuracy in noisy settings.

Contribution

It introduces a general framework for noisy importance sampling and derives new optimal proposal densities that incorporate noise variance information.

Findings

Optimal proposals adapt to noise variance regions.

Comparison shows improvements over previous methods.

Framework enhances robustness of importance sampling under noise.

Abstract

In this work, we analyze the noisy importance sampling (IS), i.e., IS working with noisy evaluations of the target density. We present the general framework and derive optimal proposal densities for noisy IS estimators. The optimal proposals incorporate the information of the variance of the noisy realizations, proposing points in regions where the noise power is higher. We also compare the use of the optimal proposals with previous optimality approaches considered in a noisy IS framework.