Abstract
Maximum likelihood estimation is a fundamental computational task in statistics. We address this problem for manifolds of low rank matrices. These represent mixtures of independent distributions of two discrete random variables. This non-convex optimization problems lead to some beautiful geometry, topology, and combinatorics. We discuss methods for finding the global maximum of the likelihood function, we present a duality theorem due to Draisma and Rodriguez, and we share recent work with Kubkas and Robeva concerning nonnegative rank and the EM algorithm.
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