报告人简介：冯阳博士，现就职于美国哥伦比亚大学统计系，任副教授。他本科毕业于中国科学技术大学少年班, 2010年获得普林斯顿大学运筹与金融工程系理学博士学位，师从国际著名统计学家范剑青教授。冯教授的研究兴趣主要包括高维统计学习，网络模型，非参数、半参数方法以及生物信息学等等。他现在是Journal of Business and Economic Statistics, Statistica Sinica， Computational Statistics and Data Analysis 以及 Statistical Analysis and Data Mining的副主编。
报告题目： Are there any community structure in a hypergraph?
摘要：Many complex networks in the real world can be formulated as hypergraphs where community detection has been widely used. However, the fundamental question of whether communities exist or not in an observed hypergraph still remains unresolved. The aim of the present work is to tackle this important problem. Specifically, we study when a hypergraph with community structure can be successfully distinguished from its counterpart, and propose concrete test statistics based on hypergraph cycles when the models are distinguishable. Our contributions are summarized as follows. For uniform hypergraphs, we show that successful testing is always impossible when average degree tends to zero, might be possible when the average degree is bounded, and is possible when the average degree is growing. We obtain asymptotic distributions of the proposed test statistics and analyze their power. Our results for growing degree case are further extended to nonuniform hypergraphs in which a new test involving both edge and hyperedge information is proposed. The novel aspect of our new test is that it is provably more powerful than the classic test involving only edge information. Simulation and real data analysis support our theoretical findings.