報告題目
Are there any community structure in a hypergraph?
報告人簡介
馮陽博士
現就職於美國哥倫比亞大學統計系，任副教授。
本科畢業於中國科學技術大學少年班, 2010年獲得普林斯頓大學運籌與金融工程系理學博士學位，師從國際著名統計學家範劍青教授。
研究興趣主要包括高維統計學習，網絡模型，非參數、半參數方法以及生物信息學等等。
現在是Journal of Business and Economic Statistics, Statistica Sinica， Computational Statistics and Data Analysis 以及 Statistical Analysis and Data Mining的副主編。
時間地點
2019年01月15日週四
上午10:30
西南交通大學犀浦校區
X2511
文章摘要
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.
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