A mirror descent approach to maximum likelihood estimation in latent variable models

TL;DR

This paper presents a mirror descent and SMC-based method for joint parameter inference and posterior estimation in latent variable models, effective for discrete and real-valued latent spaces.

Contribution

It introduces a novel mirror descent approach combined with SMC, enabling inference in models with discrete latent variables, unlike traditional methods.

Findings

Outperforms standard expectation maximisation algorithms.

Competitive with popular methods for real-valued latent variables.

Provides detailed theoretical analysis of the algorithm.

Abstract

We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the parameter space and the space of probability distributions and, contrary to other popular approaches, can be implemented when the latent variable takes values in discrete spaces. We provide a detailed theoretical analysis of both the mirror descent algorithm and its approximation via SMC. We experimentally show that the proposed algorithm outperforms standard expectation maximisation algorithms and is competitive with other popular methods for real-valued latent variables.