Tempered, Anti-trunctated, Multiple Importance Sampling

TL;DR

This paper introduces TAMIS, an adaptive importance sampling algorithm that combines tempering and anti-truncation transformations to improve efficiency and robustness without increasing target evaluations.

Contribution

The paper proposes TAMIS, a novel adaptive importance sampling method that automatically tunes proposals using tempering and anti-truncation, enhancing robustness and scalability.

Findings

Robustness to poor initial proposals

No additional target density evaluations needed

Scales well with high-dimensional problems

Abstract

Importance sampling is a Monte Carlo method that introduces a proposal distribution to sample the space according to the target distribution. Yet calibration of the proposal distribution is essential to achieving efficiency, thus the resort to adaptive algorithms to tune this distribution. In the paper, we propose a new adpative importance sampling scheme, named Tempered Anti-truncated Adaptive Multiple Importance Sampling (TAMIS) algorithm. We combine a tempering scheme and a new nonlinear transformation of the weights we named anti-truncation. For efficiency, we were also concerned not to increase the number of evaluations of the target density. As a result, our proposal is an automatically tuned sequential algorithm that is robust to poor initial proposals, does not require gradient computations and scales well with the dimension.