Modern Non-Linear Function-on-Function Regression

Abstract

We introduce a new class of non-linear function-on-function regression models for functional data using neural networks. We propose a framework using a hidden layer consisting of continuous neurons, called a continuous hidden layer, for functional response modeling and give two model fitting strategies, Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN). Both are designed explicitly to exploit the structure inherent in functional data and capture the complex relations existing between the functional predictors and the functional response. We fit these models by deriving functional gradients and implement regularization techniques for more parsimonious results. We demonstrate the power and flexibility of our proposed method in handling complex functional models through extensive simulation studies as well as real data examples.

6 figures, 6 tables (including supplementary material), 16 pages (including supplementary material). arXiv admin note: text overlap with arXiv:2104.09371

References in corpus (6)

• Functional single index models for longitudinal data
• Optimal Penalized Function-on-Function Regression under a Reproducing Kernel Hilbert Space Framework
• Non-linear Functional Modeling using Neural Networks
• Remaining Useful Life Estimation Using Functional Data Analysis
• Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs
• Manifold Data Analysis with Applications to High-Frequency 3D Imaging