A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians

Sanjoy Dasgupta, Leonard Schulman; 8(Feb):203--226, 2007.

Abstract

We show that, given data from a mixture of k well-separated spherical Gaussians in ℜ^d, a simple two-round variant of EM will, with high probability, learn the parameters of the Gaussians to near-optimal precision, if the dimension is high (d >> ln k). We relate this to previous theoretical and empirical work on the EM algorithm.

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