ABSTRACT

We present a methodology for integrating functional data into deep 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 a 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 relationship between the functional covariate and scalar response; these results were confirmed through real data applications and simulation studies. An R package (FuncNN) has also been developed on top of Keras, a popular deep learning library—this allows for general use of the approach. A supplemental document, the data and R codes are available online.

摘要

我们提出了一种将功能数据集成到深度神经网络中的方法。该模型是为具有多个函数和标量协变量的标量响应定义的。该方法的副产品是一组可以在优化过程中可视化的动态函数权重。这种可视化导致协变量与相对于传统神经网络的响应之间的关系具有更大的可解释性。该模型在许多情况下表现良好，包括新数据的预测和功能协变量与标量响应之间真实潜在关系的恢复；这些结果已通过实际数据应用和模拟研究得到证实。还在Keras之上开发了一个 R 包 ( FuncNN )，一个流行的深度学习库——这允许该方法的一般使用。补充文件、数据和 R 代码可在线获取。