Non-linear Functional Modeling using Neural Networks
This work addresses a gap in applying deep learning to functional data, which is incremental as it adapts existing neural network concepts to a specific domain.
The authors tackled the problem of modeling functional data with non-linear models by introducing two neural network frameworks, FDNN and FBNN, designed to exploit functional structure, and demonstrated their effectiveness through simulations and real data examples.
We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two variations of our framework: a functional neural network with continuous hidden layers, called the Functional Direct Neural Network (FDNN), and a second version that utilizes basis expansions and continuous hidden layers, called the Functional Basis Neural Network (FBNN). Both are designed explicitly to exploit the structure inherent in functional data. To fit these models we derive a functional gradient based optimization algorithm. The effectiveness of the proposed methods in handling complex functional models is demonstrated by comprehensive simulation studies and real data examples.