Nonlinear Algebra and Statistics (NLASTATS) Seminar by Aida Maraj: Staged Tree Models with Toric Structure

Speaker: Aida Maraj, University of Michigan

Title: Staged Tree Models with Toric Structure

Abstract: Staged tree models are discrete statistical models encoding relationships between events that generalize Bayesian networks. Relationships between events are encoded in a directed rooted tree with colored vertices. These event based models are often used in public health, medicine, risk analysis and policing.  In algebro-geometric terms, the model consists of points inside a toric variety whose design matrix is determined by the root to leaf paths in the tree. For certain trees, called balanced, Duarte and Görgen proved that the model is in fact the intersection of the toric variety and the probability simplex. The toric structure gives the model a straightforward description, and has computational advantages; it provides a Gröbner basis of binomial quadratics completely determined by the paths in the tree. In this talk we show that the class of staged tree models with a toric structure extends far outside of the balanced case, if we allow a change of coordinates. The change of coordinates and the new binomial equation rely on the combinatorics of the tree. The talk is based on joint work with Christiane Görgen and Lisa Nicklasson.

 

Nonlinear Algebra and Statistics seminar