Structured Matrix Estimation and Completion

2017/07/07 by Klopp, Olga, Lu, Yu, Tsybakov, Alexandre B. +1
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1707.02090

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.

Related

• Structured Matrix Learning under Arbitrary Entrywise Dependence and Estimation of Markov Transition Kernel
• Sharp Bounds for Multiple Models in Matrix Completion
• Transfer Learning for Matrix Completion
• Survey of Matrix Completion Algorithms
• Optimal rates of convergence for covariance matrix estimation