- 控制理论和非线性滤波讨论班

A Bridge between Invariant Theory and Maximum Likelihood Estimation

组织者

丘成栋

演讲者

康家熠

时间

2024年11月13日 21:00 至 21:30

地点

Online

摘要

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.

演讲者介绍

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025. His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.