Robust Matrix Completion with Mixed Data Types

TL;DR

This paper introduces a new computationally feasible method for low rank matrix completion that handles mixed data types with strong theoretical guarantees and parallelizable algorithms.

Contribution

It presents a novel one-step approach for recovering low rank matrices with mixed data types, extending prior methods to more general data distributions.

Findings

Method achieves strong recovery guarantees.

Algorithm is suitable for parallel computation.

Simulation results validate theoretical claims.

Abstract

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong statistical guarantees for the case where the underlying distribution of data in the matrix is continuous. A few recent approaches have extended using similar ideas these estimators to the case where the underlying distributions belongs to the exponential family. Most of these approaches assume that there is only one underlying distribution and the low rank constraint is regularized by the matrix Schatten Norm. We propose a computationally feasible statistical approach with strong recovery guarantees along with an algorithmic framework suited for parallelization to recover a low rank matrix with partially observed entries for mixed data types in one step. We also provide extensive simulation evidence that corroborate our theoretical results.