Probability matrices, non-negative rank, and parameterizations of mixture models

TL;DR

This paper introduces minimal-parameter families for non-negative matrices of rank at most two and explores their connection to mixture models for contingency tables, advancing statistical model parameterizations.

Contribution

It provides new, efficient parameterizations for low-rank non-negative matrices and links these to mixture models in statistics.

Findings

Minimal parameterizations for rank-two matrices

Connection established between matrix parameterizations and mixture models

Enhanced understanding of statistical model structures

Abstract

In this paper we parameterize non-negative matrices of sum one and rank at most two. More precisely, we give a family of parameterizations using the least possible number of parameters. We also show how these parameterizations relate to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables.