2015/10/15 by Carlos Améndola, Jean‐Charles Faugère, Jean-Charles Faugère +1 · 58 citations
Computer Science · Mathematics · Medicine · #Algebra over a field #Algebraic number #Algebraic variety #Applied mathematics #Computational chemistry #Covariance #Cumulant #Gaussian #Mathematical analysis #Mathematics #Maximum likelihood #Moment (physics) #Multivariate statistics #Phytoestrogen effects and research #Polynomial and algebraic computation #Pure mathematics #Statistics #Tensor decomposition and applications #Univariate #Variety (cybernetics) #math.AG #math.ST #stat.TH
paper · pdf · doi:10.18409/jas.v7i1.42
published in Journal of Algebraic Statistics 7(1) · 17 pages, 2 figures
arxiv created 2015/10/15 · openalex publication_date 2016/07/12 · arxiv updated 2017/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The points of a moment variety are the vectors of all moments up to some order, for a givenfamily 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 algebrato recover the parameters from the moments. Our moment varieties extend objects familiar to algebraicgeometers. For instance, the secant varieties of Veronese varieties are the loci obtained by setting allcovariance matrices to zero. We compute the ideals of the 5-dimensional moment varieties representingmixtures of two univariate Gaussians, and we oer a comparison to the maximum likelihood approach.