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Title: Doubly functional graphical models in high dimensions Authors:  Xinghao Qiao - London School of Economics (United Kingdom)
Cheng Qian - London School of Economics and Political Science (United Kingdom)
Gareth James - University of Southern California (United States) [presenting]
Abstract: The problem of estimating a functional graphical model from a data set consisting of functional observations is considered. Recent work in this area has focused on modelling dynamic graphs from high dimensional but time-varying-distributed scalar data. However, many real world examples require the construction of networks for multivariate functional data. We present a novel perspective by treating dynamic edge sets, which, for Gaussian data, correspond to dynamic sparse precision matrices, as functional objects, linking the concept of dynamics with multivariate functional data. A class of doubly functional graphical models is proposed to capture this evolving conditional dependence relationship among multiple random functions. Our approach first estimates a functional covariance matrix, and then computes sparse precision matrices, which in turn provide the doubly functional graphical model.