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Title: Nonparametric regression with network data Authors:  Swati Chandna - Birkbeck, University of London (United Kingdom) [presenting]
Pierre-Andre Maugis - University College London (United Kingdom)
Abstract: Nonparametric methods are introduced which address the setting where a sample of small networks, along with additional information, is observed. For example, in a connectome study, for each individual in the sample both a structural brain network is observed, along with covariates such as age, gender, etc. We work under the framework of exchangeability commonly used to model network data where the node labels carry no information. Under this formulation, estimation of the limit object termed `graphon', has attracted significant attention in the nonparametric literature on networks. Building upon the standard graphon model, we provide a framework that can test for any given node presenting significantly different behavior across different values of the covariates. Further, we find that although a significant portion of the graphon literature focuses on block-model approximations of the graphon, in our setting full nonparametric inference is possible and computationally tractable. We illustrate our approach using a set of brain network observations from multiple individuals.