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Journal Articles Journal of Algebraic Statistics Year : 2016

Moment Varieties of Gaussian Mixtures

Abstract

The points of a moment variety are the vectors of all moments up to some order, for a given family of probability distributions. We study the moment varieties for mixtures of multivariate Gaussians. Following up on Pearson's classical work from 1894, we apply current tools from computational algebra to recover the parameters from the moments. Our moment varieties extend objects familiar to algebraic geometers. For instance, the secant varieties of Veronese varieties are the loci obtained by setting all covariance matrices to zero. We compute the ideals of the 5-dimensional moment varieties representing mixtures of two univariate Gaussians, and we o er a comparison to the maximum likelihood approach.

Dates and versions

hal-01565874 , version 1 (20-07-2017)

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Carlos Amendola, Jean-Charles Faugere, Bernd Sturmfels. Moment Varieties of Gaussian Mixtures. Journal of Algebraic Statistics, 2016, 7 (1), ⟨10.18409/jas.v7i1.42⟩. ⟨hal-01565874⟩
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