Maximum likelihood for matrices with rank constraints

Bernd Sturmfels
2014 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14  
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We determine the maximum likelihood degree for a range of determinantal varieties, and we apply numerical algebraic geometry to compute all critical points of their likelihood functions. This led to the discovery of maximum likelihood duality between matrices of
more » ... between matrices of complementary ranks, a result proved subsequently by Draisma and Rodriguez.
doi:10.1145/2608628.2627490 dblp:conf/issac/Sturmfels14 fatcat:dqfhomahqbgh5nmkqzthuggkji