Enhanced Mixture Population Monte Carlo Via Stochastic Optimization and Markov Chain Monte Carlo Sampling

Abstract

The population Monte Carlo (PMC) algorithm is a popular adaptive importance sampling (AIS) method used for approximate computation of intractable integrals. Over the years, many advances have been made in the theory and implementation of PMC schemes. The mixture PMC (M-PMC) algorithm, for instance, optimizes the parameters of a mixture proposal distribution in a way that minimizes that Kullback-Leibler divergence to the target distribution. The parameters in M-PMC are updated using a single step of expectation maximization (EM), which limits its accuracy. In this work, we introduce a novel M-PMC algorithm that optimizes the parameters of a mixture proposal distribution, where parameter updates are resolved via stochastic optimization instead of EM. The stochastic gradients w.r.t. each of the mixture parameters are approximated using a population of Markov chain Monte Carlo samplers. We validate the proposed scheme via numerical simulations on an example where the considered target distribution is multimodal.