May 27, 2014, 4:00pm
Elina Robeva, Department of Mathematics, UC Berkeley.
Fixed Points of the EM Algorithm and Nonnegative Rank Boundaries
Abstract: Matrices of nonnegative rank $r$ represent mixtures of $r$ independent distributions for two random variables. Likelihood inference for this model leads to problems in real algebraic geometry that we address in this paper. We characterize the set of fixed points of Expectation Maximization, and we study the boundary of the space of matrices with nonnegative rank at most $3$. Both of these correspond to algebraic varieties with many irreducible components.