Low-rank matrix recovery via nonconvex optimization methods with application to errors-in-variables matrix regression
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909437539647488 |
|---|---|
| author | Li, Xin Wu, Dongya |
| author_facet | Li, Xin Wu, Dongya |
| contents | We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of regularity conditions on the nonconvex loss function and the regularizer. This recovery bound can be much tighter than that of the convex nuclear norm regularized method when some of the singular values are larger than a threshold defined by the nonconvex regularizer. In addition, we consider the errors-in-variables matrix regression as an application of the nonconvex optimization method. Probabilistic consequences and the advantage of the nonoconvex method are demonstrated through verifying the regularity conditions for specific models with additive noise and missing data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low-rank matrix recovery via nonconvex optimization methods with application to errors-in-variables matrix regression Li, Xin Wu, Dongya Optimization and Control Statistics Theory We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of regularity conditions on the nonconvex loss function and the regularizer. This recovery bound can be much tighter than that of the convex nuclear norm regularized method when some of the singular values are larger than a threshold defined by the nonconvex regularizer. In addition, we consider the errors-in-variables matrix regression as an application of the nonconvex optimization method. Probabilistic consequences and the advantage of the nonoconvex method are demonstrated through verifying the regularity conditions for specific models with additive noise and missing data. |
| title | Low-rank matrix recovery via nonconvex optimization methods with application to errors-in-variables matrix regression |
| topic | Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2412.16263 |