Structured Matrix Estimation and Completion

TL;DR

This paper develops a unified theoretical framework for matrix estimation and completion, deriving optimal convergence rates for various models including Gaussian mixtures, biclustering, and dictionary learning.

Contribution

It introduces a general framework that encompasses multiple models and establishes minimax optimal convergence rates for matrix estimation under this framework.

Findings

Derived minimax optimal rates for matrix estimation.

Unified analysis applicable to multiple models.

Achieved theoretical bounds for convergence rates.

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.