Sharp Bounds for Multiple Models in Matrix Completion
Abstract
In this paper, we demonstrate how a class of advanced matrix concentration inequalities, introduced in 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.
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