## Probability and Statistics Seminar - Keith Levin - Bootstrapping Networks with Latent Geometric Structure

- Calendar
- Mathematics & Statistics

- Date
- 01.14.2020 3:30 pm - 4:30 pm

### Description

HH 102

Dr Keith Levin, University of Michigan

Title: Bootstrapping Networks with Latent Geometric Structure

Abstract: 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. We propose two methods for obtaining bootstrap samples for networks drawn from latent space models, a class of network models in which unobserved geometric structure drives network topology. The first of these two bootstrap methods leverages the structure of these models to generate bootstrap samples of whole networks. The second method generates bootstrap samples of network statistics that are expressible as U-statistics in the latent geometry,a class of functions that includes subgraph densities and a number of other useful network summaries. We prove the consistency of both of the proposed bootstrap methods under the random dot product graph, a latent space model that includes the popular stochastic block model as a special case, though our methods are applicable to any latent space model in which the latent geometry can be recovered suitably accurately. If time allows, we will briefly discuss ongoing work applying these new bootstrap techniques to problems in neuroimaging.

Dr Keith Levin, University of Michigan

Title: Bootstrapping Networks with Latent Geometric Structure

Abstract: 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. We propose two methods for obtaining bootstrap samples for networks drawn from latent space models, a class of network models in which unobserved geometric structure drives network topology. The first of these two bootstrap methods leverages the structure of these models to generate bootstrap samples of whole networks. The second method generates bootstrap samples of network statistics that are expressible as U-statistics in the latent geometry,a class of functions that includes subgraph densities and a number of other useful network summaries. We prove the consistency of both of the proposed bootstrap methods under the random dot product graph, a latent space model that includes the popular stochastic block model as a special case, though our methods are applicable to any latent space model in which the latent geometry can be recovered suitably accurately. If time allows, we will briefly discuss ongoing work applying these new bootstrap techniques to problems in neuroimaging.

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