统计与数据科学系系列学术报告之四百五十期

时间：2024年9月19日（星期四）14:30-15:30

地点：史带楼604室

主持人：复旦大学管理学院统计与数据科学系朱仲义教授

报告人：Prof. Ji Zhu University of Michigan–Ann Arbor

题目：A Latent Space Model for Hypergraphs with Diversity and Heterogeneous Popularity

摘要： While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, i.e., those between two individuals. This work addresses the less studied, though commonly encountered, polyadic relations that can involve more than two individuals. In particular, we propose a new latent space model for hypergraphs using determinantal point processes, which is driven by the diversity within hyperedges and each node's popularity. This model mechanism is in contrast to existing hypergraph models, which are predominantly driven by similarity rather than diversity. Additionally, the proposed model accommodates broad types of hypergraphs, with no restriction on the cardinality and multiplicity of hyperedges. Consistency and asymptotic normality of the maximum likelihood estimates of the model parameters have been established. The proof is challenging, owing to the special configuration of the parameter space. Simulation studies and an application to the What's Cooking data show the effectiveness of the proposed model.

个人简介：Ji Zhu is the Susan A. Murphy Professor of Statistics at the University of Michigan, Ann Arbor. He received his B.Sc. in Physics from Peking University, China in 1996 and M.Sc. and Ph.D. in Statistics from Stanford University in 2000 and 2003, respectively. His primary research interests include statistical machine learning, high-dimensional data modeling, statistical network analysis, and their applications to health and natural sciences. He received an NSF CAREER Award in 2008 and was elected as a Fellow of the American Statistical Association in 2013 and a Fellow of the Institute of Mathematical Statistics in 2015. From 2014 to 2020, he was recognized as an ISI Highly Cited Researcher by Web of Science, which annually lists leading researchers in the sciences and social sciences worldwide. He also received the International Chinese Statistical Association Pao-Lu Hsu Award in 2022. He currently serves as the Editor-in-Chief of the Annals of Applied Statistics.