Towards Adaptive Self-Normalized Importance Samplers

TL;DR

This paper introduces a novel adaptive importance sampling framework that uses MCMC to approximate the optimal self-normalized importance sampling proposal, improving efficiency in Monte Carlo estimations.

Contribution

It presents the first AIS framework specifically targeting the SNIS optimal proposal, connecting adaptive schemes in importance sampling and ratio importance sampling.

Findings

Framework effectively approximates the optimal SNIS proposal

Connections established between AIS and adaptive RIS methods

Demonstrated improved performance in numerical experiments

Abstract

The self-normalized importance sampling (SNIS) estimator is a Monte Carlo estimator widely used to approximate expectations in statistical signal processing and machine learning. The efficiency of SNIS depends on the choice of proposal, but selecting a good proposal is typically unfeasible. In particular, most of the existing adaptive IS (AIS) literature overlooks the optimal SNIS proposal. In this paper, we introduce an AIS framework that uses MCMC to approximate the optimal SNIS proposal within an iterative scheme. This is, to the best of our knowledge, the first AIS framework targeting specifically the SNIS optimal proposal. We find a close connection with adaptive schemes used in ratio importance sampling (RIS), which also brings a new perspective and paves the way for combining techniques from AIS and adaptive RIS. We outline possible extensions, connections with existing MCMC-driven AIS algorithms, theoretical directions, and demonstrate performance in numerical examples.