PREVIOUS SEMINAR - 2nd July 2021
Speaker: Kevin Lin (University of Pennsylvania)
Title: Time-varying stochastic block models, with application to understanding the dynamics of gene co-expression
Abstract - Single-cell data enables us to investigate how gene co-expression patterns change as cells develop across time. While this question is multifaceted, we focus on understanding the theory behind a particular subtask in this talk: clustering nodes across many undirected labeled graphs indexed by time, also known as multilayer networks. Specifically, we discuss two stochastic block model (SBM) settings: one where the true connectivities among the clusters change over time while the true nodes' cluster memberships are held fixed, and another where both the SBMs' true node memberships and cluster connectivities vary smoothly across time. Our estimator is based on averaging the appropriately-debiased squared adjacency matrices followed by spectral clustering, and we demonstrate how our theoretical results improve upon the existing regimes-of-consistency (in terms of clustering error) as well as the rates-of-convergence in the literature. These results demonstrate the interplay among the number of nodes and graphs, the graph sparsity, and the rate-of-change in true cluster memberships or cluster connectivities across layers. We then demonstrate how our estimator performs empirically on single-cell data. This is a joint work with Jing Lei.