Quasi-independence models with rational maximum likelihood estimator. (May 2021)

• Record Type: Journal Article
• Authors: Coons, Jane Ivy; Sullivant, Seth
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 917
• Page End: 941
• Publication Date: 2021-05
• Subjects: Algebraic statistics -- Maximum likelihood estimation -- Quasi-independence models -- Log-linear models -- Maximum likelihood degree; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.10.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We classify the two-way quasi-independence models (independence models with structural zeros) that have rational maximum likelihood estimators, or MLEs. We give a necessary and sufficient condition on the bipartite graph associated to the model for the MLE to be rational. In this case, we give an explicit formula for the MLE in terms of combinatorial features of this graph. We also use the Horn uniformization to show that for general log-linear models M with rational MLE, any model obtained by restricting to a face of the cone of sufficient statistics of M also has rational MLE.