Disentangling Gaussians By Adam Tauman Kalai, Ankur Moitra, and Gregory Valiant 1. inTRoDucTion The Gaussian mixture model (GMM) is one of the oldest and most widely used statistical models. It is comprised of a weighted combination of heterogeneous Gaussian sources. As a simple one-dimensional example, consider measurements of heights of adults in a certain population, where the distribution of heights can be closely approximated as a mixture of two univariate Gaussians, one for males and one for females.3 Can one recover the parameters of the Gaussians from unlabeled height measurements alone (with no gender information)? Our work focuses on the case where the mixture consists of a small but unknown number of Gaussian components that may overlap the combined density may even have a single peak, as in the height example, and the dimensionality may be high. Much of the previous work on this problem attempts to learn the parameters through clustering, and consequently needs to make a strong separation assumption on the components in the mixture. The primary contribution of our research is to avoid this assumption by instead basing our learning algorithm upon the algebraic structure of the mixture. Our algorithm succeeds even if the
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Disentangling Gaussians
Kalai, Adam Tauman; Moitra, Ankur; Valiant, Gregory
Follow Communications of the ACM
, Volume 55 (2)
Association for Computing Machinery – Feb 1, 2012
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