Moment Varieties of Gaussian Mixtures
Abstract
The points of a moment variety are the vectors of all moments up to some order of a family of probability distributions. We study this variety for mixtures of 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 5dimensional moment varieties representing mixtures of two univariate Gaussians, and we offer a comparison to the maximum likelihood approach.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.04654
 Bibcode:
 2015arXiv151004654A
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Statistics Theory
 EPrint:
 17 pages, 2 figures