Optimal tuning-free convex relaxation for noisy matrix completion

Yuepeng Yang; Cong Ma

doi:10.1109/tit.2023.3284341

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arXiv · 2207.05802

Optimal tuning-free convex relaxation for noisy matrix completion

Yuepeng Yang·Cong Ma

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Abstract

This paper is concerned with noisy matrix completion--the problem of recovering a low-rank matrix from partial and noisy entries. Under uniform sampling and incoherence assumptions, we prove that a tuning-free square-root matrix completion estimator (square-root MC) achieves optimal statistical performance for solving the noisy matrix completion problem. Similar to the square-root Lasso estimator in high-dimensional linear regression, square-root MC does not rely on the knowledge of the size of the noise. While solving square-root MC is a convex program, our statistical analysis of square-root MC hinges on its intimate connections to a nonconvex rank-constrained estimator.

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BibTeX RIS

Yuepeng Yang, Cong Ma. 2022-07-12. Optimal tuning-free convex relaxation for noisy matrix completion. https://doi.org/10.1109/tit.2023.3284341

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