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Title: Non-parametric regression for networks Authors:  Katie Severn - University of Nottingham (United Kingdom) [presenting]
Ian Dryden - University of Nottingham (United Kingdom)
Simon Preston - University of Nottingham (United Kingdom)
Abstract: Dynamic network data are becoming increasingly available, for example, social networks representing social interactions over time. Hence there is a need to develop a suitable methodology for the statistical analysis of networks which are conditional on time. Motivated by these dynamic networks, we provide a general framework to estimate a regression curve from a sample of networks which are conditional on a set of Euclidean covariates. In this framework, networks are identified by their graph Laplacian matrices, for which metrics, embeddings, tangent spaces, and a projection from Euclidean space to the space of graph Laplacians are defined. We develop an adapted Nadaraya-Watson estimator for the graph Laplacian matrices and show this has uniform weak consistency for estimation using Euclidean and power Euclidean metrics. The methodology is applied to the Enron email corpus to model smooth trends in monthly networks and highlight anomalous networks.