Robust Functional Basis Neural Network Method With the Normalization

ABSTRACT This paper aims to develop a robust nonlinear model utilizing neural networks for function‐on‐function regression problems. The proposed framework is designed to enhance robustness in regression modeling by minimizing the impact of outliers in the response variable during model training. To achieve this, we introduce a robust loss function tailored to handle outliers effectively applied within a neural network based on basis expansion, and propose a novel functional normalization technique that normalizes the input function values of hidden layers with respect to time points. This approach demonstrates faster convergence as compared to existing neural network models and is less sensitive to hyperparameter settings. It also achieves high performance regression results even with outliers in the response variable. The effectiveness and superiority of the proposed method are validated through extensive simulation studies and real‐world applications using COVID‐19 excess mortality data.