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Title: Estimation and bootstrapping for collections of low-rank networks Authors:  Keith Levin - University of Wisconsin (United States) [presenting]
Abstract: In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across networks. For example, in neuroimaging, fMRI studies yield graphs whose vertices correspond to brain regions, which are the same across subjects. We consider the setting where a collection of networks share a low-rank mean structure but may differ in the noise structure on their edges. We introduce a weighted network average for estimating the low-rank structure under this setting, which we conjecture to be minimax. The utility of this estimate for inference is illustrated on synthetic networks and on data from an fMRI study of schizophrenia. We then turn to the problem of bootstrapping under this and related models for generating collections of low-rank networks. This problem raises interesting questions concerning how to conduct resampling in latent space network models.