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2010
ACM

Efficiently Learning Mixtures of Two Gaussians

12 years 3 months ago
Efficiently Learning Mixtures of Two Gaussians
Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We provide a polynomial-time algorithm for this problem for the case of two Gaussians in n dimensions (even if they overlap), with provably minimal assumptions on the Gaussians, and polynomial data requirements. In statistical terms, our estimator converges at an inverse polynomial rate, and no such estimator (even exponential time) was known for this problem (even in one dimension). Our algorithm reduces the n-dimensional problem to the one-dimensional problem, where the method of moments is applied. One technical challenge is proving that noisy estimates of the first six moments of a univariate mixture suffice to recover accurate estimates of the mixture parameters, as conjectured by Pearson (1894), and in fact these estimates converge at an inverse polynomial rate. As a corollary, we can efficiently perform near-optimal clustering: in the case where the overl...
Adam Tauman Kalai, Ankur Moitra, and Gregory Valia
Added 09 Aug 2010
Updated 09 Aug 2010
Type Conference
Year 2010
Where STOC
Authors Adam Tauman Kalai, Ankur Moitra, and Gregory Valiant
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