Gaussian mixture identifiability from degree 6 moments
Year: 2024
Type: article
Abstract: We resolve most cases of identifiability from sixth-order moments for Gaussian mixtures on spaces of large dimensions. Our results imply that for a mixture of $m$ Gaussians on an $n$-dimensional space, the means and covariances can be uniquely recovered from the mixture moments of degree 6, as long as $m$ is bounded by some function in $Ω(n^4)$. The constant hidden in the $\mathscr{O}$-notation is optimal and equals the one in the upper bound from counting parameters. We give an argument that degree-$4$ moments never suffice in any nontrivial case, and we conduct some numerical experiments indicating that degree $5$ is minimal for identifiability.
Source: Algebraic Statistics
Author: Alexander Taveira Blomenhofer
Institutions: University of Copenhagen, Centrum Wiskunde & Informatica
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405240796