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A Stochastic Path-Integrated Differential EstimatoR Expectation Maximization Algorithm

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 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 E-step, adapted from the stochastic path-integrated differential estimator (SPIDER) technique. We derive finite-time complexity bounds for smooth non-convex likelihood: we show that for convergence to an ǫ-approximate stationary point, the complexity scales as K Opt (n, ǫ) = O(ǫ −1) and K CE (n, ǫ) = n + √ nO(ǫ −1), where K Opt (n, ǫ) and K CE (n, ǫ) are respectively the number of 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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https://hal.archives-ouvertes.fr/hal-03029700
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Submitted on : Saturday, November 28, 2020 - 7:27:22 PM
Last modification on : Wednesday, June 1, 2022 - 4:30:15 AM

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  • HAL Id : hal-03029700, version 1

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Gersende Fort, Eric Moulines, Hoi-To Wai. A Stochastic Path-Integrated Differential EstimatoR Expectation Maximization Algorithm. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtuel, Canada. ⟨hal-03029700⟩

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