SIMPLE-RC: Group Network Inference with Non-Sharp Nulls and Weak Signals

Jinchi Lv

<p>Large-scale network inference with uncertainty quantification has important applications in natural, social, and medical sciences. The recent work of Fan, Fan, Han, and Lv (2022) introduced a general framework of statistical inference on membership profiles in large networks (SIMPLE) for testing the sharp null hypothesis that a pair of given nodes share the same membership profile. In real applications, there are often groups of nodes under investigation that may share similar membership profiles in the presence of relatively weaker signals than the setting considered in SIMPLE. To address these practical challenges, in this paper, we propose a SIMPLE method with random coupling (SIMPLE-RC) for testing the non-sharp composite null hypothesis that a group of given nodes shares similar (not necessarily identical) membership profiles under weaker signals. Utilizing the idea of random coupling, we construct our test as the maximum of the SIMPLE tests for subsampled node pairs from the group. Such a technique significantly reduces the correlation among individual SIMPLE tests while largely maintaining the power, enabling delicate analysis of the asymptotic distributions of the SIMPLE-RC test. Our method and theory cover both the cases with and without node degree heterogeneity. These new theoretical developments are empowered by a second-order expansion of spiked eigenvectors under the $\ell_\infty$-norm, built upon our work for random matrices with weak spikes. Our theoretical results and the practical advantages of the newly proposed method are demonstrated through simulations and real data examples.&nbsp;</p>

2024-03-28 (Thursday) 10:00-11:30

Room N302, Economics Building

English

厦门大学研究生院、经济学院、王亚南经济研究院、邹至庄经济研究院

独立讲座

Jingyuan Liu

<div>Jinchi Lv is Kenneth King Stonier Chair in Business Administration, Department Chair, Professor in Data Sciences and Operations Department of the Marshall School of Business at the University of Southern California, and Professor in Department of Mathematics at USC. He received his Ph.D. in Mathematics from Princeton University in 2007. He was McAlister Associate Professor in Business Administration at USC from 2016-2019. His research interests include statistics, machine learning, data science, business applications, and artificial intelligence and blockchain.</div> <div>&nbsp;</div> <div>His papers have been published in journals in statistics, economics, business, computer science, information theory, neuroscience, and biology. He is the recipient of Distinguished Scholar (2024, Lingnan University), NSF Grant (2023), NSF Emerging Frontiers (EF) Grant (2022), Fellow of American Statistical Association (2020), NSF Grant (2020), Kenneth King Stonier Chair in Business Administration (2019), Fellow of Institute of Mathematical Statistics (2019), Member of USC University Committee on Appointments, Promotions, and Tenure (UCAPT, 2019-present), USC Marshall Dean's Award for Research Impact (2017), Adobe Data Science Research Award (2017), McAlister Associate Professor in Business Administration (2016), Simons Foundation Grant (2016), the Royal Statistical Society Guy Medal in Bronze (2015), NSF Faculty Early Career Development (CAREER) Award (2010), USC Marshall Dean's Award for Research Excellence (2009), Journal of the Royal Statistical Society Series B Discussion Paper (2008), NSF Grant (2008), and Zumberge Individual Award from USC's James H. Zumberge Faculty Research and Innovation Fund (2008). He has served as an associate editor of Operations Research (2024-present), Journal of the American Statistical Association (2023-present), Journal of Business &amp; Economic Statistics (2018-present), The Annals of Statistics (2013-2018), and Statistica Sinica (2008-2016).</div>

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