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MiS Preprint

Algebraic Identifiability of Gaussian Mixtures

Carlos Amendola, Kristian Ranestad and Bernd Sturmfels


We prove that all moment varieties of univariate Gaussian mixtures have the expected dimension. Our approach rests on intersection theory and Terracini's classification of defective surfaces. The analogous identifiability result is shown to be false for mixtures of Gaussians in dimension three and higher. Their moments up to third order define projective varieties that are defective. Our geometric study suggests an extension of the Alexander-Hirschowitz Theorem for Veronese varieties to the Gaussian setting.

Dec 4, 2016
Dec 5, 2016
MSC Codes:
mixture models, secant variety, Gaussian

Related publications

2018 Repository Open Access
Carlos Améndola, Kristian Ranestad and Bernd Sturmfels

Algebraic identifiability of Gaussian mixtures

In: International mathematics research notices, 2018 (2018) 21, pp. 6556-6580