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February 2015 Matrix estimation by Universal Singular Value Thresholding
Sourav Chatterjee
Ann. Statist. 43(1): 177-214 (February 2015). DOI: 10.1214/14-AOS1272

Abstract

Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially after the pioneering works of Emmanuel Candès and collaborators. This paper introduces a simple estimation procedure, called Universal Singular Value Thresholding (USVT), that works for any matrix that has “a little bit of structure.” Surprisingly, this simple estimator achieves the minimax error rate up to a constant factor. The method is applied to solve problems related to low rank matrix estimation, blockmodels, distance matrix completion, latent space models, positive definite matrix completion, graphon estimation and generalized Bradley–Terry models for pairwise comparison.

Citation

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Sourav Chatterjee. "Matrix estimation by Universal Singular Value Thresholding." Ann. Statist. 43 (1) 177 - 214, February 2015. https://doi.org/10.1214/14-AOS1272

Information

Published: February 2015
First available in Project Euclid: 9 December 2014

zbMATH: 1308.62038
MathSciNet: MR3285604
Digital Object Identifier: 10.1214/14-AOS1272

Subjects:
Primary: 62F12, 62G05
Secondary: 05C99, 60B20

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 1 • February 2015
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