Pair Correlation Factor and the Sample Complexity of Gaussian Mixtures
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913976507432960 |
|---|---|
| author | Aryan, Farzad |
| author_facet | Aryan, Farzad |
| contents | We study the problem of learning Gaussian Mixture Models (GMMs) and ask: which structural properties govern their sample complexity? Prior work has largely tied this complexity to the minimum pairwise separation between components, but we demonstrate this view is incomplete.
We introduce the \emph{Pair Correlation Factor} (PCF), a geometric quantity capturing the clustering of component means. Unlike the minimum gap, the PCF more accurately dictates the difficulty of parameter recovery.
In the uniform spherical case, we give an algorithm with improved sample complexity bounds, showing when more than the usual $ε^{-2}$ samples are necessary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pair Correlation Factor and the Sample Complexity of Gaussian Mixtures Aryan, Farzad Machine Learning 62H30, 68T05, 62F12, 68Q32 I.2.6; G.3 We study the problem of learning Gaussian Mixture Models (GMMs) and ask: which structural properties govern their sample complexity? Prior work has largely tied this complexity to the minimum pairwise separation between components, but we demonstrate this view is incomplete. We introduce the \emph{Pair Correlation Factor} (PCF), a geometric quantity capturing the clustering of component means. Unlike the minimum gap, the PCF more accurately dictates the difficulty of parameter recovery. In the uniform spherical case, we give an algorithm with improved sample complexity bounds, showing when more than the usual $ε^{-2}$ samples are necessary. |
| title | Pair Correlation Factor and the Sample Complexity of Gaussian Mixtures |
| topic | Machine Learning 62H30, 68T05, 62F12, 68Q32 I.2.6; G.3 |
| url | https://arxiv.org/abs/2508.03633 |