On EM algorithms and their proximal generalizations

TL;DR

This paper reinterprets the EM algorithm as a proximal point method, introduces a new Kullback-proximal generalization, and analyzes convergence properties, especially for boundary cluster points.

Contribution

It provides a novel proximal framework for EM algorithms, offering new convergence insights and handling boundary cluster points.

Findings

Proximal interpretation of EM algorithms.

Introduction of Kullback-proximal algorithms.

Analysis of boundary cluster points.

Abstract

In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in \cite{Chretien&Hero:98} and called Kullback-proximal algorithms. The proximal framework allows us to prove new results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space.