Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2018
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1803.00679 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914623829049344 |
|---|---|
| author | O'Rourke, Sean Vu, Van Wang, Ke |
| author_facet | O'Rourke, Sean Vu, Van Wang, Ke |
| contents | The Davis-Kahan-Wedin $\sin Θ$ theorem describes how the singular subspaces of a matrix change when subjected to a small perturbation. This classic result is sharp in the worst case scenario. In this paper, we prove a stochastic version of the Davis-Kahan-Wedin $\sin Θ$ theorem when the perturbation is a Gaussian random matrix. Under certain structural assumptions, we obtain an optimal bound that significantly improves upon the classic Davis-Kahan-Wedin $\sin Θ$ theorem. One of our key tools is a new perturbation bound for the singular values, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_00679 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Matrices with Gaussian noise: optimal estimates for singular subspace perturbation O'Rourke, Sean Vu, Van Wang, Ke Machine Learning Information Theory Probability The Davis-Kahan-Wedin $\sin Θ$ theorem describes how the singular subspaces of a matrix change when subjected to a small perturbation. This classic result is sharp in the worst case scenario. In this paper, we prove a stochastic version of the Davis-Kahan-Wedin $\sin Θ$ theorem when the perturbation is a Gaussian random matrix. Under certain structural assumptions, we obtain an optimal bound that significantly improves upon the classic Davis-Kahan-Wedin $\sin Θ$ theorem. One of our key tools is a new perturbation bound for the singular values, which may be of independent interest. |
| title | Matrices with Gaussian noise: optimal estimates for singular subspace perturbation |
| topic | Machine Learning Information Theory Probability |
| url | https://arxiv.org/abs/1803.00679 |