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Poster

A Stochastic Path Integral Differential EstimatoR Expectation Maximization Algorithm

Gersende Fort · Eric Moulines · Hoi-To Wai

Poster Session 5 #1443

Abstract: The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called {\tt SPIDER-EM}, for inference from a training set of size n, n1. At the core of our algorithm is an estimator of the full conditional expectation in the {\sf E}-step, adapted from the stochastic path integral differential estimator ({\tt SPIDER}) technique. We derive finite-time complexity bounds for smooth non-convex likelihood: we show that for convergence to an ϵ-approximate stationary point, the complexity scales as KOpt(n,ϵ)=O(ϵ1) and KCE(n,ϵ)=n+nO(ϵ1), where KOpt(n,ϵ) and KCE(n,ϵ) are respectively the number of {\sf M}-steps and the number of per-sample conditional expectations evaluations. This improves over the state-of-the-art algorithms. Numerical results support our findings.

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