MATRIX ESTIMATION BY UNIVERSAL SINGULAR VALUE THRESHOLDING

• 成果类型: Article
• 署名作者: Chatterjee, Sourav
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1272
• 发表日期: 2015
• 页码: 177-214
• 关键词: stochastic blockmodels; completion; graphs; algorithms; MODEL; Penalization; prediction; number; NORM

摘要

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 Candes 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.