Past Event: Oden Institute Seminar

Estimating Gaussian mixtures using sparse polynomial moment systems

Julia Lindberg, Postdoc, Bernd Sturmfels, Max Planck Institute, Leipzig Germany, and starting January 2023: Bing Instructor, Department of Mathematics, UT Austin

Abstract

 The method of moments is a statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding identifiability asks how many moment equations are needed to get finitely many solutions and how many solutions there are. We answer this question for classes of Gaussian mixture models using the tools of polyhedral geometry. Using these results, we present a homotopy method to perform parameter recovery, and therefore density estimation, for high dimensional Gaussian mixture models. The number of paths tracked in our method scales linearly in the dimension.

Biography

Julia Lindberg is a postdoc in the nonlinear algebra group at the Max Planck Institute in Leipzig Germany. She graduated with a PhD in Electrical and Computer Engineering from the University of Wisconsin-Madison (UW) in May of 2022. Her research is broadly in applied algebraic geometry and has focused on applications in statistics, optimization and power systems engineering. She was the recipient of the John Nohel award for an outstanding thesis in applied math, the Excellence in Mathematical Research Prize, the Grainger Graduate Student Fellowship and the Sarah and Dave Epstein Fellowship. Prior to her graduate studies she completed a M.S. in math and a B.S. in math and dance, all from UW.  She becomes a Bing Instructor in the Mathematics Department at UT Austin in January of 2023.