Gaussian Mixture Identifiability from degree 6 Moments
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929622204022784 |
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| author | Blomenhofer, Alexander Taveira |
| author_facet | Blomenhofer, Alexander Taveira |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03850 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gaussian Mixture Identifiability from degree 6 Moments Blomenhofer, Alexander Taveira Algebraic Geometry Statistics Theory primary: 14N07, secondary: 15A69, 62H12 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. |
| title | Gaussian Mixture Identifiability from degree 6 Moments |
| topic | Algebraic Geometry Statistics Theory primary: 14N07, secondary: 15A69, 62H12 |
| url | https://arxiv.org/abs/2307.03850 |