Adaptive Annealed Importance Sampling with Constant Rate Progress

TL;DR

This paper introduces CR-AIS, an adaptive annealed importance sampling method that dynamically adjusts the annealing schedule based on distribution difficulty, improving efficiency and reducing tuning needs.

Contribution

The paper derives a constant rate discretization schedule for AIS, extends it to f-divergences, and proposes the CR-AIS algorithm with efficient implementation.

Findings

CR-AIS performs well on benchmark distributions.

It avoids costly tuning loops of existing adaptive methods.

The method adapts the annealing schedule to distribution difficulty.

Abstract

Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution given its unnormalized density function. This algorithm relies on a sequence of interpolating distributions bridging the target to an initial tractable distribution such as the well-known geometric mean path of unnormalized distributions which is assumed to be suboptimal in general. In this paper, we prove that the geometric annealing corresponds to the distribution path that minimizes the KL divergence between the current particle distribution and the desired target when the feasible change in the particle distribution is constrained. Following this observation, we derive the constant rate discretization schedule for this annealing sequence, which adjusts the schedule to the difficulty of moving samples between the initial and the target distributions. We further extend our results to $f$-divergences and present the respective dynamics of annealing sequences based on which we propose the Constant Rate AIS (CR-AIS) algorithm and its efficient implementation for $\alpha$-divergences. We empirically show that CR-AIS performs well on multiple benchmark distributions while avoiding the computationally expensive tuning loop in existing Adaptive AIS.