Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)
Gersende Fort, Eric Moulines, Hoi-To Wai
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, n≫1. 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(ϵ−1) and KCE(n,ϵ)=n+√nO(ϵ−1), 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.