Deep Learning with Functional Inputs

TL;DR

This paper introduces a novel deep learning approach that incorporates functional data, providing interpretable dynamic weights and demonstrating strong predictive performance through real and simulated data applications.

Contribution

It develops a new methodology for integrating functional data into neural networks, enhancing interpretability and applicability in various contexts.

Findings

Effective prediction of new data

Successful recovery of true functional weights

Enhanced interpretability of covariate-response relationships

Abstract

We present a methodology for integrating functional data into deep densely connected feed-forward neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set of dynamic functional weights that can be visualized during the optimization process. This visualization leads to greater interpretability of the relationship between the covariates and the response relative to conventional neural networks. The model is shown to perform well in a number of contexts including prediction of new data and recovery of the true underlying functional weights; these results were confirmed through real applications and simulation studies. A forthcoming R package is developed on top of a popular deep learning library (Keras) allowing for general use of the approach.