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Keywords: Functional data analysis; Neural networks; Nonparametric regression; Rate of convergence; ReLU activation function; ADNI database.
In this work, we propose a deep neural networks based method to perform nonparametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with ReLU activation function. We provide the convergence rate of the proposed deep neural networks estimator in terms of the empirical norm. We discuss how to properly select of the architecture parameters by cross-validation. Through Monte Carlo simulation studies we examine the finite-sample performance of the proposed method. Finally, the proposed method is applied to analyze positron emission tomography images of patients with Alzheimer disease obtained from the Alzheimer Disease Neuroimaging Initiative database.