Simple Relative Deviation Bounds for Covariance and Gram Matrices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913860246568960 |
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| author | Barzilai, Daniel Shamir, Ohad |
| author_facet | Barzilai, Daniel Shamir, Ohad |
| contents | We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our results provide sharper control across the spectrum. Our analysis is based on a general-purpose theorem that allows one to convert existing uniform bounds into relative ones. The theorems and techniques emphasize simplicity and should be applicable across various settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05754 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple Relative Deviation Bounds for Covariance and Gram Matrices Barzilai, Daniel Shamir, Ohad Probability Machine Learning Statistics Theory We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our results provide sharper control across the spectrum. Our analysis is based on a general-purpose theorem that allows one to convert existing uniform bounds into relative ones. The theorems and techniques emphasize simplicity and should be applicable across various settings. |
| title | Simple Relative Deviation Bounds for Covariance and Gram Matrices |
| topic | Probability Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2410.05754 |