A Stochastic Path-Integrated Differential EstimatoR Expectation Maximization Algorithm

• URL: http://arxiv.org/abs/2012.01929v1
• Date: Mon, 30 Nov 2020 15:49:31 GMT
• Title: A Stochastic Path-Integrated Differential EstimatoR Expectation Maximization Algorithm
• Authors: Gersende Fort (IMT), Eric Moulines (X-DEP-MATHAPP), Hoi-To Wai
• Abstract summary: 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, called textttSP, for inference from a conditional expectation estimator.
• Score: 19.216497414060658
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \texttt{SPIDER-EM}, for inference from a training set of size $n$, $n \gg 1$. At the core of our algorithm is an estimator of the full conditional expectation in the {\sf E}-step, adapted from the stochastic path-integrated differential estimator ({\tt SPIDER}) technique. We derive finite-time complexity bounds for smooth non-convex likelihood: we show that for convergence to an $\epsilon$-approximate stationary point, the complexity scales as $K_{\operatorname{Opt}} (n,\epsilon )={\cal O}(\epsilon^{-1})$ and $K_{\operatorname{CE}}( n,\epsilon ) = n+ \sqrt{n} {\cal O}(\epsilon^{-1} )$, where $K_{\operatorname{Opt}}( n,\epsilon )$ and $K_{\operatorname{CE}}(n, \epsilon )$ 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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