Structured Matrix Estimation and Completion
Statistics Theory
2017-07-10 v1 Statistics Theory
Abstract
We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and dictionary learning. We consider 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 obtain minimax optimal rates of convergence for various special models.
Cite
@article{arxiv.1707.02090,
title = {Structured Matrix Estimation and Completion},
author = {Olga Klopp and Yu Lu and Alexandre B. Tsybakov and Harrison H. Zhou},
journal= {arXiv preprint arXiv:1707.02090},
year = {2017}
}