# Estimation of the Mean Function of Functional Data via Deep Neural Networks

arXiv: https://arxiv.org/abs/2012.04573 · HTML: https://mlsanity.com/paper/2012.04573/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2020.

## Built on by (most cited first, 8 of 8)

- [Calibrating multi-dimensional complex ODE from noisy data via deep neural networks](https://mlsanity.com/paper/2106.03591/) (2021)
- [Deep Feature Screening: Feature Selection for Ultra High-Dimensional Data via Deep Neural Networks](https://mlsanity.com/paper/2204.01682/) (2022)
- [Deep Neural Network Classifier for Multi-dimensional Functional Data](https://mlsanity.com/paper/2205.08592/) (2022)
- [CovNet: Covariance Networks for Functional Data on Multidimensional Domains](https://mlsanity.com/paper/2104.05021/) (2021)
- [Robust Deep Neural Network Estimation for Multi-dimensional Functional Data](https://mlsanity.com/paper/2205.09604/) (2022)
- [Multiclass classification for multidimensional functional data through deep neural networks](https://mlsanity.com/paper/2305.13349/) (2023)
- [Nonparametric regression with modified ReLU networks](https://mlsanity.com/paper/2207.08306/) (2022)
- [Enhancing Functional Data Analysis with Sequential Neural Networks: Advantages and Comparative Study](https://mlsanity.com/paper/2311.01875/) (2023)

## Abstract (arXiv)

In this work, we propose a deep neural network method to perform nonparametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with ReLU activation function. By properly choosing network architecture, our estimator achieves the optimal nonparametric convergence rate in empirical norm. Under certain circumstances such as trigonometric polynomial kernel and a sufficiently large sampling frequency, the convergence rate is even faster than root-n rate. 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.