Bootstrapping Networks with Latent Geometric Structure (Keith Levin - University of Michigan)

Starts: 4:00 pm on Thursday, January 23, 2020
Ends: 5:00 pm on Thursday, January 23, 2020
Location: MCS B39

A core problem in statistical network analysis is to develop network analogues of classical statistical techniques. The problem of bootstrapping network data stands out as especially challenging, owing to the dependency structure of network data and the fact that one typically observes only a single network, rather than a sample. In this talk, I will present a method for generating bootstrap samples for networks drawn from latent space models, a class of network models in which unobserved geometric structure drives network topology. We show consistency of the proposed bootstrap method under the random dot product graph, a latent space model that includes the popular stochastic blockmodel as a special case, though the method is applicable to any latent space model in which the latent geometry can be recovered suitably accurately. In the second half of the talk, I will outline a few ongoing projects applying this bootstrap method and several related network analysis techniques to neuroscientific data obtained from fMRI studies. Common to these projects is the presence of latent low-dimensional network structure that we wish to relate to patient-level covariates such as age or disease status.