A0937
Title: Deep neural network for functional graphical models structure learning
Authors: Shuoyang Wang - University of Louisville (United States) [presenting]
Abstract: Functional data refers to data that are realizations of random functions varying over a continuum, such as images or signals. In many modern fields, including neuroscience, medical science, and traffic monitoring, observations are better modeled as multivariate random functions rather than as vectors. To capture the conditional independence structure of such multivariate functional data, functional graphical models have been developed. A novel and flexible method is proposed to estimate the neighborhood of each node using a deep neural network-based functional data regression and feature selection approach with an arbitrary nonparametric form. The full graph structure is then recovered by combining the estimated neighborhoods. The approach avoids common distributional assumptions on the random functions and circumvents the need for a well-defined precision operator, which may not exist in the functional data context. Furthermore, model consistency is established for the proposed algorithm. The convergence rate reaches the classical nonparametric regression rate up to a logarithmic factor. A novel critical sampling frequency is discovered that governs the convergence rates of the deep neural network estimator. The empirical performance of the method is demonstrated through simulation studies and a real data application.
