# Robust Deep Neural Network Estimation for Multi-dimensional Functional Data

arXiv: https://arxiv.org/abs/2205.09604 · HTML: https://mlsanity.com/paper/2205.09604/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [A Selective Overview of Deep Learning](https://mlsanity.com/paper/1904.05526/) (2019)
- [On Deep Instrumental Variables Estimate](https://mlsanity.com/paper/2004.14954/) (2020)
- [Deep Learning with Functional Inputs](https://mlsanity.com/paper/2006.09590/) (2020)
- [Optimal Nonparametric Inference via Deep Neural Network](https://mlsanity.com/paper/1902.01687/) (2019)
- [Estimation of the Mean Function of Functional Data via Deep Neural Networks](https://mlsanity.com/paper/2012.04573/) (2020)
- [Multi-dimensional Functional Principal Component Analysis](https://mlsanity.com/paper/1510.04439/) (2015)

## Built on by (most cited first, 2 of 2)

- [Robust deep learning from weakly dependent data](https://mlsanity.com/paper/2405.05081/) (2024)
- [A least distance estimator for a multivariate regression model using deep neural networks](https://mlsanity.com/paper/2401.03123/) (2024)

## Abstract (arXiv)

In this paper, we propose a robust estimator for the location function from multi-dimensional functional data. The proposed estimators are based on the deep neural networks with ReLU activation function. At the meanwhile, the estimators are less susceptible to outlying observations and model-misspecification. For any multi-dimensional functional data, we provide the uniform convergence rates for the proposed robust deep neural networks estimators. Simulation studies illustrate the competitive performance of the robust deep neural network estimators on regular data and their superior performance on data that contain anomalies. The proposed method is also applied to analyze 2D and 3D images of patients with Alzheimer's disease obtained from the Alzheimer Disease Neuroimaging Initiative database.