Moment varieties of the inverse Gaussian and gamma distributions are nondefective

Abstract

We show that the parameters of a $k$-mixture of inverse Gaussian or gamma distributions are algebraically identifiable from the first $3k-1$ moments, and rationally identifiable from the first $3k+2$ moments. Our proofs are based on Terracini's classification of defective surfaces, careful analysis of the intersection theory of moment varieties, and a recent result on sufficient conditions for rational identifiability of secant varieties by Massarenti--Mella.

24 pages. Minor corrections and expository improvements. To appear in J. Symb. Comput

References in corpus (6)

• The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
• Non-defectivity of Segre-Veronese varieties
• Identifiability for mixtures of centered Gaussians and sums of powers of quadratics
• Generalized identifiability of sums of squares
• Moment varieties from inverse Gaussian and gamma distributions
• Gaussian Mixture Identifiability from degree 6 Moments