Geom-SPIDER-EM: Faster Variance Reduced Stochastic Expectation Maximization for Nonconvex Finite-Sum Optimization

TL;DR

This paper introduces Geom-SPIDER-EM, an accelerated stochastic EM algorithm that reduces computational costs for large-scale nonconvex latent variable models, achieving state-of-the-art complexity bounds.

Contribution

It extends SPIDER-EM with geometric acceleration, providing faster convergence guarantees for nonconvex finite-sum optimization problems.

Findings

Achieves state-of-the-art complexity bounds.

Provides conditions for linear convergence.

Numerical results confirm theoretical advantages.

Abstract

The Expectation Maximization (EM) algorithm is a key reference for inference in latent variable models; unfortunately, its computational cost is prohibitive in the large scale learning setting. In this paper, we propose an extension of the Stochastic Path-Integrated Differential EstimatoR EM (SPIDER-EM) and derive complexity bounds for this novel algorithm, designed to solve smooth nonconvex finite-sum optimization problems. We show that it reaches the same state of the art complexity bounds as SPIDER-EM; and provide conditions for a linear rate of convergence. Numerical results support our findings.