Group Network Inference with Non-Sharp Nulls and Weak Signals中国科学院数学与系统科学研究院应用数学研究所

Group Network Inference with Non-Sharp Nulls and Weak Signals

Speaker:	杨帆博士,清华大学
Inviter:
Title:	Group Network Inference with Non-Sharp Nulls and Weak Signals
Time & Venue:	2023.10.27 9:00 N613
Abstract:	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 profiles. In real applications, there are often groups of nodes under investigation that may share similar membership profiles at the presence of relatively weaker signals than the setting considered in SIMPLE. To address these practical challenges, we propose a SIMPLE method with random coupling (SIMPLE-RC) for testing the non-sharp null hypothesis that a group of given nodes share 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 technique reduces significantly the correlation among individual SIMPLE tests while largely maintaining the power, enabling delicate analysis on the asymptotic distributions of the SIMPLE-RC test. These new theoretical developments are empowered by a second-order expansion of spiked eigenvectors, built upon our work for random matrices with weak spikes. Based on joint work with Jianqing Fan, Yingying Fan and Jinchi Lv.
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