Abstract

Given a statistical model and some observed data, an important problem is identifying the parameters of the model that make the observed data the most probable. These parameters are encoded in the Maximum Likelihood Estimate (MLE) given the observed data. However, an MLE given observed data does not necessarily exist, and even if it does it may not be unique, in other words it may not be identifiable. The aim of this talk is to explain how complete collineations (a concept from algebraic geometry) can be used to resolve non-identifiability of the MLE in the case of Directed Acyclic Graphical models. More precisely, I will show how given initial data, choosing a complete collineation based on this data produces a perturbation of the data, which can in turn be used to obtain a unique MLE given the initial data. Time permitting, I will outline open questions regarding statistical interpretations of the moduli space of complete collineations. This is joint work with Gergely Berczi, Philipp Reichenbach and Anna Seigal.