Joint Statistics and Applied Mathematics Colloquium: Julia Lindberg (UT Austin)
applied algebra & convex geometry
Location
Sondheim Hall : 409
Date & Time
February 17, 2025, 12:00 pm – 1:00 pm
Description
Title: Leveraging algebraic structures for innovations in data science and complex systems
Abstract: Applied algebraic geometry is a subfield of applied mathematics that utilizes concepts, tools, and techniques from algebraic geometry to solve problems in various applied sciences. It blends tools from algebraic geometry, optimization, and statistics to develop certifiable computational algebraic methods to address modern engineeering challenges.
In this talk, I will showcase the power of these methods in solving problems related to Gaussian mixture models (GMMs). In the first part of the talk I will discuss a statistical technique for parameter recovery called the method of moments. I will discuss how to leverage algebraic techniques to design scalable and certifiable moment-based methods for parameter recovery of GMMs. In the second part of this talk, I will discuss recent work relating to Gaussian Voronoi cells. This work introduces new geometric perspectives with implications for high-dimensional data analysis. I will also touch on how these methods complement my broader research in polynomial optimization and power systems engineering.