An Adaptive Resample-Move Algorithm for Estimating Normalizing Constants

TL;DR

This paper introduces an adaptive Resample-Move algorithm that dynamically adjusts particle numbers during sequential Monte Carlo sampling, resulting in more accurate and resource-efficient estimation of normalizing constants.

Contribution

The paper proposes an adaptive Resample-Move algorithm that improves normalizing constant estimation by dynamically expanding particles based on distribution approximation needs.

Findings

ARM achieves lower variance in estimates.

ARM uses fewer computational resources.

ARM is easier to tune than AIS.

Abstract

The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard choice of using a fixed number of particles at each iteration is suboptimal because some steps will contribute disproportionately to the variance of the estimate. We introduce an adaptive version of the Resample-Move algorithm, in which the particle set is adaptively expanded whenever a better approximation of an intermediate distribution is needed. The algorithm builds on the expression for the optimal number of particles and the corresponding minimum variance found under ideal conditions. Benchmark results on challenging Gaussian Process Classification and Restricted Boltzmann Machine applications show that Adaptive Resample-Move (ARM) estimates the normalizing constant with a smaller variance, using less computational resources, than either Resample-Move with a fixed number of particles or Annealed Importance Sampling. A further advantage over Annealed Importance Sampling is that ARM is easier to tune.