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Published February 2007 | Published
Journal Article Open

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


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.

Additional Information

© 2007 Sanjoy Dasgupta and Leonard Schulman. The first author is indebted to Daniel Hsu for suggesting many simplifications to the analysis, to the reviewers for significantly improving the presentation, and to the NSF for support under grant IIS-0347646.

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Published - DASjmlr07.pdf


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October 16, 2023