A probabilistic algorithm for computing data-discriminants of likelihood equations. (November 2017) - Rodriguez, Jose Israel; Tang, Xiaoxian
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.