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Yulia Alexandr: Logarithmic Voronoi cell for Gaussian models

Time: Tue 2022-05-10 16.15

Location: D31, Lindstedtsvägen 5, and Zoom

Video link: Meeting ID: 659 3743 5667

Lecturer: Yulia Alexandr (UC Berkeley)

Abstract

In this talk, I will introduce the theory of logarithmic Voronoi cells for Gaussian models. I will start by defining logarithmic Voronoi cells in the discrete statistical setting and briefly discussing their properties. Then we will look at how logarithmic Voronoi cells generalize for continuous distributions. More precisely, a logarithmic Voronoi cell at a point on a Gaussian model is a convex set contained in its log-normal spectrahedron. We will see that for both directed and undirected graphical models the two sets coincide. For the latter family, I will introduce a decomposition theory of logarithmic Voronoi cells. We will also study covariance models, for which logarithmic Voronoi cells are, in general, strictly contained in log-normal spectrahedra. We will look at the bivariate correlation model in detail.

This talk is based on joint work with Serkan Hosten.