Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.13199 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918370310356992 |
|---|---|
| author | Liu, Dali Weng, Haolei |
| author_facet | Liu, Dali Weng, Haolei |
| contents | In this paper, we demonstrate how a class of advanced matrix concentration inequalities, introduced in \cite{brailovskaya2024universality}, can be used to eliminate the dimensional factor in the convergence rate of matrix completion. This dimensional factor represents a significant gap between the upper bound and the minimax lower bound, especially in high dimension. Through a more precise spectral norm analysis, we remove the dimensional factors for three popular matrix completion estimators, thereby establishing their minimax rate optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13199 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp Bounds for Multiple Models in Matrix Completion Liu, Dali Weng, Haolei Statistics Theory In this paper, we demonstrate how a class of advanced matrix concentration inequalities, introduced in \cite{brailovskaya2024universality}, can be used to eliminate the dimensional factor in the convergence rate of matrix completion. This dimensional factor represents a significant gap between the upper bound and the minimax lower bound, especially in high dimension. Through a more precise spectral norm analysis, we remove the dimensional factors for three popular matrix completion estimators, thereby establishing their minimax rate optimality. |
| title | Sharp Bounds for Multiple Models in Matrix Completion |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2411.13199 |