In this work, we propose a deep neural networks-based method to perform non-parametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with rectifier linear unit (ReLU) activation function. We provide the convergence rate of the proposed deep neural networks estimator in terms of the empirical norm. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyse positron emission tomography images of patients with Alzheimer's disease obtained from the Alzheimer Disease Neuroimaging Initiative database.

中文翻译：

---

通过深度神经网络估计功能数据的平均函数

在这项工作中，我们提出了一种基于深度神经网络的方法来对功能数据执行非参数回归。所提出的估计器基于具有整流器线性单元 (ReLU) 激活函数的稀疏连接的深度神经网络。我们根据经验范数提供了所提出的深度神经网络估计器的收敛速度。通过蒙特卡罗模拟研究，我们检查了所提出方法的有限样本性能。最后，将所提出的方法应用于分析从阿尔茨海默病神经成像倡议数据库中获得的阿尔茨海默病患者的正电子发射断层扫描图像。