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

2020/11/24 by Gersende Fort, Fort, Gersende, Moulines, Eric +2
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2011.12392

openalex publication_date 2020/11/24 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28

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.

Citations

• Convergence of a stochastic approximation version of the EM algorithm
• Gradient-based learning applied to document recognition
• PAGE: A Simple and Optimal Probabilistic Gradient Estimator for Nonconvex Optimization

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