Alternating Bregman projections and convergence of the EM algorithm

TL;DR

This paper analyzes the convergence behavior of alternating Bregman projections between non-convex sets and applies these findings to establish convergence of certain EM algorithm variants for non-convex parameter spaces.

Contribution

It provides a theoretical framework for convergence of Bregman projections in non-convex settings and demonstrates how this applies to EM algorithms.

Findings

Convergence to intersection points or gap points is proven.

Convergence speed is generally sub-linear, but can be linear under transversality.

Applied analysis confirms convergence of EM variants for non-convex parameters.

Abstract

We investigate convergence of alternating Bregman projections between non-convex sets and prove convergence to a point in the intersection, or to points realizing a gap between the two sets. The speed of convergence is generally sub-linear, but may be linear under transversality. We apply our analysis to prove convergence of versions of the expectation maximization algorithm for non-convex parameter sets.