Abstract: Conditional independence models for Gaussian random variables are algebraic varieties in the cone of positive definite covariance matrices. We explore the structure of these varieties in the case of Bayesian networks (graphical models on directed acyclic graphs) with a view towards generalizing the recursive factorization theorem to situations with hidden random variables. Among the familiar algebraic varieties that appear as special cases are secant varieties, matrix Schubert varieties, and toric degenerations of the Grassmannian.

Note that the speaker will be also be giving a talk in the MBI Lecture Series (in cooperation with the Algebraic Statistics Seminar) at 1:30pm in Jennings Hall, Room 355.