Title
Some Results on Network Modeling
Abstract
The block-model family has four popular network models: SBM, MMSBM, DCBM, and DCMM. A fundamental problem is, how well each of these models fits with real networks. We propose GoF-MSCORE as a new Goodness-of-Fit (GoF) metric for DCMM (the broadest one among the four), with two main ideas. The first is to use cycle count statistics as a general recipe for GoF. The second is a novel network fitting scheme. GoF-MSCORE is a flexible GoF approach. We adapt it to all four models
in the block-model family.
We show that for each of the four models, if the assumed model is correct, then the corresponding GoF metric converges to N(0,1) as the network sizes diverge. We also analyze the powers and show that these metrics are optimal in many settings. For 11 frequently-used real networks, we use the proposed GoF metrics to show that DCMM fits well with almost all of them. We also show that SBM, DCBM, and MMSBM do not fit well with many of these networks, especially when the networks are relatively large.
Bio
Jiashun Jin is Professor in Statistics and Affiliated Professor in Machine Learning at Carnegie Mellon University. His expertise is in statistical inference for Rare and Weak signals in Big Data. His earlier work was on large-scale multiple testing, focusing on the development of (Tukey's) Higher Criticism and practical False Discovery Rate (FDR) controlling methods. His more recent interest is on the analysis of social networks and text documents. Jin is an elected IMS fellow and an elected ASA fellow. He has also delivered the highly selective IMS Medallion Lecture in 2015 and IMS AoAS (Annals of Applied Statistics) Lecture in 2016. Jin has co-authored three Editor's Invited Review papers and three Editor's Invited Discussion papers. He has served as Associate Editor for several statistical journals including Annals of Statistics and JASA, and he is currently severing IMS as the IMS Treasurer.
