Title: Optimal tuning-free convex relaxation for noisy matrix completion
Authors: Yuepeng Yang - University of Chicago (United States)
Cong Ma - University of Chicago (United States) [presenting]
Abstract: The focus is on 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.