Title:
Ten Steps of EM Suffice for Mixtures of Two Gaussians
Ten Steps of EM Suffice for Mixtures of Two Gaussians
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Author(s)
Daskalakis, Constantinos
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Abstract
The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means clustering algorithm. Despite its wide use and applications, there are essentially no known convergence guarantees for this method. We provide global convergence guarantees for mixtures of two Gaussians with known covariance matrices. We show that EM converges geometrically to the correct mean vectors, and provide simple, closed-form expressions for the convergence rate. As a simple illustration, we show that, in one dimension, ten steps of the EM algorithm initialized at infinity result in less than 1% error estimation of the means.
(Joint work with Christos Tzamos and Manolis Zampetakis.)
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Date Issued
2017-03-06
Extent
63:35 minutes
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Moving Image
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Lecture