An adaptive mixture-population Monte Carlo method for likelihood-free inference

TL;DR

This paper introduces an adaptive mixture-population Monte Carlo method for likelihood-free variational inference, enabling efficient approximation of complex, multi-modal posterior distributions without gradient estimation.

Contribution

It develops an automatic component-updating procedure for MPMC, improving its flexibility and applicability in likelihood-free Bayesian inference.

Findings

Capable of approximating multi-modal posteriors effectively

Automatically determines the number of mixture components

Performs well with standard Gaussian initializations

Abstract

This paper focuses on variational inference with intractable likelihood functions that can be unbiasedly estimated. A flexible variational approximation based on Gaussian mixtures is developed, by adopting the mixture population Monte Carlo (MPMC) algorithm in \cite{cappe2008adaptive}. MPMC updates iteratively the parameters of mixture distributions with importance sampling computations, instead of the complicated gradient estimation of the optimization objective in usual variational Bayes. Noticing that MPMC uses a fixed number of mixture components, which is difficult to predict for real applications, we further propose an automatic component--updating procedure to derive an appropriate number of components. The derived adaptive MPMC algorithm is capable of finding good approximations of the multi-modal posterior distributions even with a standard Gaussian as the initial distribution, as demonstrated in our numerical experiments.