Maximum Likelihood for Matrices with Rank ConstraintsAlgebra & Discrete Mathematics
|Speaker:||Bernd Sturmfels, Dept. of Mathematics, UC Berkeley|
|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.