Chris Randall

My research is in algebraic statistics, which applies the tools of algebraic geometry to statistical questions. I specifically study the geometry of objects coming from the statistics of multivariate normal distributions.

My research is in algebraic statistics, which applies the tools of algebraic geometry to statistical questions. Specifically, I study the convex algebraic geometry of objects arising from maximum likelihood estimation for multivariate Gaussian distributions. I prove that so-called log-Voronoi cells of mean centered projective Gaussian models are defined by polynomial inequalities, allowing for their exact algebraic computation. Currently, I am involved in a project to extend these results to other features of metric algebraic geometry, such as curvature and bottlenecks. This project replaces the usual Euclidean distance with a statistical distance called the Kullback Leibler divergence. This distance is not symmetric or algebraic, meaning the usual results from metric algebraic geometry do not apply. However, we show that the comparison of these distances becomes algebraic when restricted to critical points, allowing for our algebraic computations.