Statistics Papers

Document Type

Journal Article

Date of this Version

12-2013

Publication Source

Journal of Machine Learning Research

Volume

14

Start Page

3619

Last Page

3647

Abstract

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is introduced and studied. The rate of convergence for the estimate is obtained. Information-theoretical methods are used to establish a minimax lower bound under the general sampling model. The minimax upper and lower bounds together yield the optimal rate of convergence for the Frobenius norm loss. Computational algorithms and numerical performance are also discussed.

Keywords

1-bit matrix completion, low-rank matrix, max-norm, trace-norm, constrained optimization, maximum likelihood estimate, optimal rate of convergence

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Date Posted: 27 November 2017

This document has been peer reviewed.