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arXiv · 2307.03850

Gaussian Mixture Identifiability from degree 6 Moments

Alexander Taveira Blomenhofer
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Abstract

We resolve most cases of identifiability from sixth-order moments for Gaussian mixtures on spaces of large dimensions. Our results imply that the parameters of a generic mixture of $ m\leq\mathcal{O}(n^4) $ Gaussians on $ \mathbb R^n $ can be uniquely recovered from the mixture moments of degree 6. The constant hidden in the $ \mathcal{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.

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Alexander Taveira Blomenhofer. 2023-07-07. Gaussian Mixture Identifiability from degree 6 Moments. https://doi.org/10.2140/astat.2025.16.1

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