一、题目

Regularized maximum likelihood in the beta model for large and sparse networks

二、主讲人

晏挺

三、摘要

The beta model is a powerful tool for modeling network generation driven by node degree heterogeneity. It is simple yet expressive nature particularly well-suits large and sparse networks, where even moderately complex models might be infeasible to fit due to very few nonzero observations and computational challenge. However, simple as this model is, our theoretical understanding remains rather limited. Also, available computation method for fitting this model remains unscalable. In a big-data era, substantial improvements are urgently needed for the beta model. Our paper brings several major refinements and improvements to the methodology and theory of the beta model: 1. we propose a new L2 penalized MLE scheme; we design a novel algorithm that can comfortably handle sparse networks of millions of nodes, sharply contrasting the best existing tools that could only deal with thousands of nodes; 2. we present much stronger error bounds on beta-models under much weaker assumptions than existing literature; we also prove the first resolution-limit bound and new normality results; 3. we apply our method to analyze a huge COVID-19 knowledge graph and discover very meaningful results.

四、主讲人介绍

晏挺，现任华中师范大学数学与统计学学院教授，博士生导师，讲授了多门主干课程，主持了4项国家自然科学基金项目。曾在乔治华盛顿大学从事博士后研究，于2013年进入华中师范大学工作，入选了湖北省楚天学者计划。目前的主要研究方向为网络模型，成对比较以及应用统计。在Annals of Statistics,Journal of the American Statistical Association, Biometrika等统计学期刊上发表论文三十余篇。

五、邀请人

林路

六、时间

11月17日（周三）10:00-11:00

七、地点

腾讯会议ID: 918 888 408

八、主办方

山东大学数学学院