2023-07-19
Gaussian mixture identifiability from degree-6 moments
Publication
Publication
Algebraic Statistics , Volume 16 - Issue 1 p. 1- 28
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 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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doi.org/10.2140/astat.2025.16.1 | |
Algebraic Statistics | |
Optimization for and with Machine Learning | |
Organisation | Networks and Optimization |
Taveira Blomenhofer, F. A. (2023). Gaussian mixture identifiability from degree-6 moments. Algebraic Statistics, 16(1), 1–28. doi:10.2140/astat.2025.16.1 |