An Invitation to Singular Learning Theory

主 讲 人 ：Daniel Windisc    博士后

活动时间：04月03日19时00分    

地      点 ：理科群1号楼D204室；线上https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1 会议 ID: 86763384947；密码: 612593

讲座内容：

This talk will give a broad introduction on a fascinating and useful connection between Bayesian statistics and resolution of singularities from algebraic geometry, discovered by Japanese statistician Sumio Watanabe. Specifically, we will focus on how real birational invariants of varieties and schemes come up in the following model selection problem that is crucial for machine learning and modern statistics: Given a data set, which is the statistical model that fits the data best?

While Watanabe's idea had been specialized to examples of statistical models, a profound mathematical treatment had been missing. Besides introducing the general theory, this talk will give recent advances concerning this foundation. In particular, we will see formulas for two real birational invariants, the real log canonical threshold and its multiplicity, that are crucial to the model selection problem, in the case of hyperplane arrangements. These are based on joint work of the author with Dimitra Kosta.

主讲人介绍：

Daniel Windisch holds a PhD in mathematics from Graz University of Technology in Austria (Dec 2022). Prior to joining the School of Mathematics at the University of Edinburgh in July 2024 as a Postdoc, he carried out his research at the Max-Planck-Institute Leipzig in the group of Bernd Sturmfels (Jan–Jun 2024) and at Graz University of Technology (Jan–Dec 2023).

His research interests range from ring theory (in particular, over non-Noetherian rings) and model theory of rings and fields to algebraic geometry and its application. Currently, his main efforts lie in establishing a well-founded mathematical theory for the connection of model selection in AI and resolution of singularities in algebraic geometry.

发布时间：2025-04-01 15:52:19