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Abstract
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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
Gaussians on an
-dimensional space,
the means and covariances can be uniquely recovered from the mixture moments of degree 6, as long as
is bounded by some
function in
. The constant
hidden in the
-notation
is optimal and equals the one in the upper bound from counting parameters. We give an argument
that degree-
moments never suffice in any nontrivial case, and we conduct some numerical experiments indicating
that degree
is minimal for identifiability.
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Keywords
secant varieties, Gaussian mixtures, Waring decomposition
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Mathematical Subject Classification
Primary: 14N07
Secondary: 15A69, 62H12
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Milestones
Received: 29 September 2023
Revised: 27 September 2024
Accepted: 30 September 2024
Published: 10 December 2024
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© 2025 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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