Algebraic Identifiability of Gaussian Mixtures

Abstract

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.

18 pages, to appear in International Mathematics Research Notices

References in corpus (1)

• Moment Varieties of Gaussian Mixtures

Cited by in corpus (6)

• Varieties of Signature Tensors
• Discrete Gaussian distributions via theta functions
• Moment Identifiability of Homoscedastic Gaussian Mixtures
• Moment varieties from inverse Gaussian and gamma distributions
• Moment varieties of the inverse Gaussian and gamma distributions are nondefective
• Autocovariance Varieties of Moving Average Random Fields