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Maximum Likelihood for Matrices with Rank Constraints

Algebra & Discrete Mathematics

Speaker: Bernd Sturmfels, Dept. of Mathematics, UC Berkeley
Location: 1147 MSB
Start time: Thu, Feb 14 2013, 3:10PM

Maximum likelihood estimation is a fundamental computational task in statistics. We discuss this problem for manifolds of low rank matrices. These represent mixtures of independent distributions of two discrete random variables. This non-convex optimization leads to some beautiful geometry, topology, and combinatorics. We explain how numerical algebraic geometry is used to find the global maximum of the likelihood function. This is joint work with Jon Hauenstein and Jose Rodriguez.