Deep Learning with Functional Inputs
This enables more interpretable neural network modeling for functional data problems, though it appears incremental as an extension of existing deep learning frameworks.
The authors developed a method to incorporate functional data into deep neural networks for scalar responses with mixed covariate types, achieving good performance in prediction and weight recovery across simulation studies and real applications.
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.