Title: Non-parametric regression for networks
Speaker: Ian Dryden (Florida International University)
Network data are becoming increasingly available, and so there is a need to develop suitable methodology for statistical analysis. Networks can be represented as graph Laplacian matrices, which are a type of manifold-valued data. Our main objective is to estimate a regression curve from a sample of graph Laplacian matrices conditional on a set of Euclidean covariates, for example in dynamic networks where the covariate is time. We develop an adapted Nadaraya-Watson estimator which has uniform weak consistency for estimation using Euclidean and power Euclidean metrics.
We apply the methodology to a study of peptide shape variation from molecular dynamics simulations, where networks are formed from the correlations between atoms. We investigate nonparametric regression of the networks versus time, and also versus a predictor measuring the change in size of the peptide. Further applications are given to an email corpus to model smooth trends in monthly networks and highlight anomalous networks. A final motivating application is given in corpus linguistics, which explores trends in an author’s writing style over time based on word co-occurrence networks.
This is joint work with Katie Severn and Simon Preston.
Ian Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami and has taught and carried out research at the University of Nottingham, University of South Carolina, University of Leeds and University of Chicago. He has 35 years research experience, and his main area of study is the development of statistical methodology in highly-structured data analysis, including shapes, images and functional data. He obtained his PhD from the University of Leeds in 1989 and served as head of the School of Mathematical Sciences, University of Nottingham from 2014-2018. He is an elected fellow of the Institute of Mathematical Statistics and was awarded a Royal Society Wolfson Research Merit Award (2012-2017).