Efficient error and variance estimation for randomized matrix computations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914961969643520 |
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| author | Epperly, Ethan N. Tropp, Joel A. |
| author_facet | Epperly, Ethan N. Tropp, Joel A. |
| contents | Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nyström approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06342 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Efficient error and variance estimation for randomized matrix computations Epperly, Ethan N. Tropp, Joel A. Numerical Analysis Machine Learning 62F40, 65F55, 68W20 Randomized matrix algorithms have become workhorse tools in scientific computing and machine learning. To use these algorithms safely in applications, they should be coupled with posterior error estimates to assess the quality of the output. To meet this need, this paper proposes two diagnostics: a leave-one-out error estimator for randomized low-rank approximations and a jackknife resampling method to estimate the variance of the output of a randomized matrix computation. Both of these diagnostics are rapid to compute for randomized low-rank approximation algorithms such as the randomized SVD and randomized Nyström approximation, and they provide useful information that can be used to assess the quality of the computed output and guide algorithmic parameter choices. |
| title | Efficient error and variance estimation for randomized matrix computations |
| topic | Numerical Analysis Machine Learning 62F40, 65F55, 68W20 |
| url | https://arxiv.org/abs/2207.06342 |