A Variational Adaptive Population Importance Sampler

Abstract

Adaptive importance sampling (AIS) methods are a family of algorithms which can be used to approximate Bayesian posterior distributions. Many AIS algorithms exist in the literature, where the differences arise in the manner by which the proposal distribution is adapted at each iteration. The adaptive population importance sampler (APIS), for example, deterministically samples from a mixture distribution and uses the local information given by the samples and weights to adapt the location parameter of each proposal. The update rules by nature are heuristic, but effective, especially in the case that the target posterior is multimodal. In this work, we introduce a novel AIS scheme which incorporates modern techniques in stochastic optimization to improve the methodology for higher-dimensional posterior inference. More specifically, we derive update rules for the parameters of each proposal by means of deterministic mixture sampling and show that the method outperforms other state-of-the-art approaches in high-dimensional scenarios.