Perturbation of matrices and non-negative rank with a view toward statistical models

TL;DR

This paper investigates how small changes to a matrix affect its non-negative rank, providing theoretical insights and connections to statistical models like mixture models and maximum likelihood estimation.

Contribution

It proves the upper-semicontinuity of non-negative rank and explores specific perturbation families, linking matrix perturbations to statistical estimation problems.

Findings

Non-negative rank is upper-semicontinuous under perturbations.

Identifies special families of matrix perturbations.

Connects matrix perturbation theory to statistical maximum likelihood estimation.

Abstract

In this paper we study how perturbing a matrix changes its non-negative rank. We prove that the non-negative rank is upper-semicontinuos and we describe some special families of perturbations. We show how our results relate to Statistics in terms of the study of Maximum Likelihood Estimation for mixture models.