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Mathematics > Statistics Theory

arXiv:2411.13199 (math)
[Submitted on 20 Nov 2024 (v1), last revised 21 Nov 2024 (this version, v2)]

Title:Sharp Bounds for Multiple Models in Matrix Completion

Authors:Dali Liu, Haolei Weng
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Abstract: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 five different estimators in various settings, thereby establishing their minimax rate optimality.
Comments: 35 pages. Several typos have been corrected. All comments are warmly welcomed
Subjects: Statistics Theory (math.ST)
Cite as: arXiv:2411.13199 [math.ST]
  (or arXiv:2411.13199v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2411.13199

Submission history

From: Dali Liu [view email]
[v1] Wed, 20 Nov 2024 10:59:30 UTC (26 KB)
[v2] Thu, 21 Nov 2024 02:32:15 UTC (26 KB)
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