Extremal bounds for Gaussian trace estimation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916493151698944 |
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| author | Hallman, Eric |
| author_facet | Hallman, Eric |
| contents | This work derives extremal tail bounds for the Gaussian trace estimator applied to a real symmetric matrix. We define a partial ordering on the eigenvalues, so that when a matrix has greater spectrum under this ordering, its estimator will have worse tail bounds. This is done for two families of matrices: positive semidefinite matrices with bounded effective rank, and indefinite matrices with bounded 2-norm and fixed Frobenius norm. In each case, the tail region is defined rigorously and is constant for a given family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extremal bounds for Gaussian trace estimation Hallman, Eric Statistics Theory Numerical Analysis Probability 60E15, 60E07, 65C05 This work derives extremal tail bounds for the Gaussian trace estimator applied to a real symmetric matrix. We define a partial ordering on the eigenvalues, so that when a matrix has greater spectrum under this ordering, its estimator will have worse tail bounds. This is done for two families of matrices: positive semidefinite matrices with bounded effective rank, and indefinite matrices with bounded 2-norm and fixed Frobenius norm. In each case, the tail region is defined rigorously and is constant for a given family. |
| title | Extremal bounds for Gaussian trace estimation |
| topic | Statistics Theory Numerical Analysis Probability 60E15, 60E07, 65C05 |
| url | https://arxiv.org/abs/2411.15454 |