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Sharp bounds for multiple models in matrix completion
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DOI：10.1214/26-EJS2503.png)
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Abstract
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In this paper, we demonstrate how a class of advanced matrix concentration inequalities, introduced in [2], 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.
Keywords:
Matrix completion
low-rank matrix estimation
minimax optimality
Journal
E
IF:
1.3
Papers:
22
Citations:
0
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Cited Papers
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ANNALS OF STATISTICS
OAAI
ANNALS OF STATISTICSIF3.7
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