Matrix Completion by the Principle of Parsimony

TL;DR

This paper extends Dempster's covariance selection method to more general matrices and demonstrates that these generalized completions solve an entropy-like variational problem, broadening the theoretical understanding of matrix completion.

Contribution

The paper generalizes Dempster's covariance selection to nonsingular and full rank rectangular matrices, linking matrix completion to entropy-like variational problems.

Findings

Generalized matrix completion methods to broader classes of matrices.

Established a connection between matrix completion and entropy-like variational problems.

Extended the theoretical framework of covariance selection.

Abstract

Dempster's covariance selection method is extended first to general nonsingular matrices and then to full rank rectangular matrices. Dempster observed that his completion solved a maximum entropy problem. We show that our generalized completions are also solutions of a suitable entropy-like variational problem.