Convergence of the EM algorithm via proximal techniques

TL;DR

This paper analyzes the convergence properties of the EM algorithm by framing it as a generalized proximal method, establishing convergence of iterates under certain mathematical conditions.

Contribution

It introduces a novel perspective by representing EM as a proximal method and proves convergence of the iterates under definability assumptions.

Findings

Convergence of EM iterates is established under o-minimal structure conditions.

The paper provides a new theoretical framework linking EM and proximal algorithms.

Convergence results are applicable to a broad class of models with definable likelihoods.

Abstract

We investigate convergence of the expectation maximization algorithm by representing it as a generalized proximal method. Convergence of iterates and not just in value is investigated under natural hypotheses such as definability of the incomplete data log-likelihood in the sense of o-minimal structure theory.