Moment Varieties of Gaussian Mixtures
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 oer a comparison to the maximum likelihood approach.