BIMSA > Seminar on Control Theory and Nonlinear Filtering A Bridge between Invariant Theory and Maximum Likelihood Estimation
A Bridge between Invariant Theory and Maximum Likelihood Estimation
Organizer
Shing Toung Yau
Speaker
Jia Yi Kang
Time
Wednesday, November 13, 2024 9:00 PM - 9:30 PM
Venue
Online
Abstract
In this talk, I will report a paper uncovered connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. They present a dictionary that relates notions of stability from geometric invariant theory to the existence and uniqueness of a maximum likelihood estimate. Their dictionary holds for both discrete and continuous statistical models: They discuss log-linear models and Gaussian models, including matrix normal models and directed Gaussian graphical models. For instance, algorithms from statistics can be used in invariant theory, and vice versa.