Robust Deep Neural Network Estimation for Multi-dimensional Functional Data

TL;DR

This paper introduces a robust deep neural network estimator for multi-dimensional functional data that is resistant to outliers and model errors, with proven convergence and superior performance in simulations and real-world neuroimaging data.

Contribution

It develops a novel robust deep neural network approach for estimating the location function in multi-dimensional functional data, with theoretical convergence guarantees.

Findings

Demonstrates uniform convergence rates for the proposed estimators.

Shows superior performance on anomalous data in simulations.

Successfully applied to 2D and 3D neuroimaging data of Alzheimer's patients.

Abstract

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.