Moment Varieties of Gaussian Mixtures
Algebraic Geometry
2017-04-06 v1 Statistics Theory
Statistics Theory
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 5-dimensional moment varieties representing mixtures of two univariate Gaussians, and we offer a comparison to the maximum likelihood approach.
Keywords
Cite
@article{arxiv.1510.04654,
title = {Moment Varieties of Gaussian Mixtures},
author = {Carlos Améndola and Jean-Charles Faugère and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1510.04654},
year = {2017}
}
Comments
17 pages, 2 figures