Biography: Tracy Ke is currently Assistant Professor of Statistics at Harvard University. She obtained her PhD in Operations Research and Financial Engineering from Princeton University in 2014, advised by Professor Jianqing Fan. From 2014 to 2018, she was Assistant Professor of Statistics at Chicago University. She joined Harvard University in 2018. Her research interests include high-dimensional statistics, machine learning, network data analysis, and text mining. In her work on high-dimensional statistics, she is particularly interested in the optimal statistical inference when the signals are very rare and weak. In her work on network data analysis, she is particularly interested in estimating the latent community structure of a network. She is the recipient of NSF CAREER Award and ASA Noether Young Scholar Award. Also see here -http://zke.fas.harvard.edu/
Title: Estimating the number of communities in a social network.
Abstract: Given a symmetric network with n nodes, how to estimate the number of communities K is a fundamental problem in social network. We propose Stepwise Goodness-of-Fit (StGoF) as a new approach to estimating K. For m = 1, 2, . . ., StGoF alternately uses a community detection step (pretending m is the correct number of communities) and a goodness-of-fit step. We use a spectral method, SCORE, for community detection, and propose a new goodness-of-fit measure. Denote the goodness-of-fit statistic in step m by ψ(m). We show that as n → ∞, ψ(m) converges to a standard normal distribution when m = K and ψ(m) goes to infinity in probability when m < K. Therefore, with a proper threshold, StGoF terminates at m = K as desired.
We consider a broad setting where we allow severe degree heterogeneity, a wide range of sparsity, and especially weak signals. In particular, we propose a measure for signal-to-noise ratio (SNR) and show that there is a phase transition: when SNR → 0 as n → ∞, consistent estimates for K do not exist, and when SNR → ∞, StGoF is consistent, uniformly for a broad class of settings. In this sense, StGoF achieves the optimal phase transition.
(Joint work with Jiashun Jin, Shengming Luo, and Minzhe Wang)