Structured Matrix Estimation and Completion

Olga Klopp (), Yu Lu (), Alexandre B. Tsybakov () and Harrison H. Zhou ()
Additional contact information
Olga Klopp: ESSEC Business School ; CREST
Yu Lu: Yale University
Alexandre B. Tsybakov: ENSAE, UMR CNRS 9194
Harrison H. Zhou: Yale University

No 2017-43, Working Papers from Center for Research in Economics and Statistics

Abstract: We study the problem of matrix estimation and matrix completion for matrices with general clustering structure. We consider an unified model which includes as particular cases gaussian mixture model, mixed membership model, bi-clustering model and dictionary learning. For this general model we obtain the optimal convergence rates in a minimax sense for estimation of the signal matrix under the Frobenius norm and under the spectral norm. As a consequence of our general result we recover minimax optimal rates of convergence for the special models mentioned before.

Keywords: matrix completion; matrix estimation; minimax optimality (search for similar items in EconPapers)
Pages: 36 pages
Date: 2017-09-15
New Economics Papers: this item is included in nep-ecm
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