A probabilistic algorithm for computing data-discriminants of likelihood equations. (November 2017)

• Record Type: Journal Article
• Authors: Rodriguez, Jose Israel; Tang, Xiaoxian
• Is Part Of: Journal of symbolic computation. Volume 83(2017)
• Page Start: 342
• Page End: 364
• Publication Date: 2017-11
• Subjects: Maximum likelihood estimation -- Likelihood equation -- Discriminant; 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.2016.11.017
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: An algebraic approach to the maximum likelihood estimation problem is to solve a very structured parameterized polynomial system called likelihood equations that have finitely many complex (real or non-real) solutions. The only solutions that are statistically meaningful are the real solutions with positive coordinates. In order to classify the parameters (data) according to the number of real/positive solutions, we study how to efficiently compute the discriminants, say data-discriminants (DD), of the likelihood equations. We develop a probabilistic algorithm with three different strategies for computing DDs. Our implemented probabilistic algorithm based onMaple andFGb is more efficient than our previous version (Rodriguez and Tang, 2015 ) and is also more efficient than the standard elimination for larger benchmarks. By applyingRAGlib to a DD we compute, we give the real root classification of 3 by 3 symmetric matrix model.