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arXiv · 1608.02280

Statistical Guarantees for Estimating the Centers of a Two-component Gaussian Mixture by EM

Jason M. Klusowski·W. D. Brinda
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Abstract

Recently, a general method for analyzing the statistical accuracy of the EM algorithm has been developed and applied to some simple latent variable models [Balakrishnan et al. 2016]. In that method, the basin of attraction for valid initialization is required to be a ball around the truth. Using Stein's Lemma, we extend these results in the case of estimating the centers of a two-component Gaussian mixture in $d$ dimensions. In particular, we significantly expand the basin of attraction to be the intersection of a half space and a ball around the origin. If the signal-to-noise ratio is at least a constant multiple of $ \sqrt{d\log d} $, we show that a random initialization strategy is feasible.

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Jason M. Klusowski, W. D. Brinda. 2016-08-07. Statistical Guarantees for Estimating the Centers of a Two-component Gaussian Mixture by EM. https://arxiv.org/abs/1608.02280

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