Abstract: This talk studies root-level community recovery in hierarchical stochastic block models using the signs of the Fiedler vector of the unnormalized graph Laplacian. The central question is whether spectral clustering remains reliable when the root-level density gap is small but lower-level communities are much denser. After reviewing a general perturbation approach for heterogeneous two-block models, I present a refined result for balanced binary-tree SBMs in a strong-leaf regime. Using a Haar-wavelet decomposition of the population Laplacian and a leave-one-out nodewise expansion, we show that the empirical Fiedler vector is ell_2-consistent and achieves exact sign recovery of the root split with high probability. The analysis indicates that multiscale connectivity heterogeneity need not hurt root-level clustering, even when the root signal is only at the logarithmic sparse scale.

Bio: Dr. Xiaodong Li is an Associate Professor in the Department of Statistics at the University of California, Davis. His research interests lie mainly in statistical learning and high-dimensional statistics. He has received several honors, including the NSF CAREER Award, the 2019 Information Theory Paper Award, and the 2022–23 UC Davis Chancellor’s Fellow award. He currently serves as an Associate Editor for the Journal of Multivariate Analysis, Sankhya A, and ASA Discoveries.