When:
Friday, May 10, 2024
11:00 AM - 12:00 PM CT
Where: Chambers Hall, Ruan Conference Room – lower level, 600 Foster St, Evanston, IL 60208 map it
Audience: Faculty/Staff - Student - Post Docs/Docs - Graduate Students
Cost: free
Contact:
Kisa Kowal
(847) 491-3974
Group: Department of Statistics and Data Science
Category: Academic, Lectures & Meetings
T-Stochastic Graphs
Karl Rohe, Professor of Statistics, University of Wisconsin-Madison
Abstract: Previous statistical approaches to hierarchical clustering for social network analysis all construct an "ultrametric" hierarchy. While the assumption of ultrametricity has been discussed and studied in the phylogenetics literature, it has not yet been acknowledged in the social network literature. We show that "non-ultrametric structure" in the network introduces significant instabilities in the existing top-down recovery algorithms. To address this issue, we introduce an instability diagnostic plot and use it to examine a collection of empirical networks. These networks appear to violate the "ultrametric" assumption. We propose a deceptively simple class of probabilistic models called T-Stochastic Graphs which impose no topological restrictions on the latent hierarchy. Perhaps surprisingly, this model generalizes the previous models. To illustrate this model, we propose six alternative forms of hierarchical network models and then show that all six are equivalent to the T-Stochastic Graph model. These alternative models motivate a novel approach to hierarchical clustering that combines spectral techniques with the well-known Neighbor-Joining algorithm from phylogenetic reconstruction. We prove this spectral approach is statistically consistent.