Distributed composite expectile regression neural network for large-scale nonlinear modeling

This paper proposes the Composite Expectile Regression Neural Network (CERNN), a unified nonlinear regression framework based on feedforward neural networks that jointly estimates the response at multiple expectile levels. By jointly optimizing asymmetric squared loss functions at several expectile levels, CERNN yields a richer description of the conditional distribution of the response, capturing central trends, asymmetric behavior, and tail-related risks. Compared with conventional Expectile Regression Neural Networks (ERNN), the CERNN framework offers greater modeling flexibility and incorporates explicit regularization together with the Bayesian Information Criterion (BIC)-based model selection to control model complexity and enhance estimation stability and generalization. To address the computational challenges arising from large-scale datasets and distributed storage, we further develop a distributed extension, termed the Distributed Composite Expectile Regression Neural Network (DCERNN). Leveraging a master-worker architecture with multi-round gradient communication, DCERNN enables scalable parallel training across computing nodes while achieving essentially the same statistical accuracy as the centralized CERNN. Extensive Monte Carlo experiments indicate that CERNN delivers superior predictive accuracy and robustness relative to ERNN and conventional squared-loss Artificial Neural Networks (ANN), particularly in the presence of complex nonlinear structures and heavy-tailed error distributions. Distributed experiments further show that DCERNN substantially reduces wall-clock training time while preserving predictive performance. Real-data applications to the BostonHousing and CaliforniaHousing datasets further confirm the effectiveness and practical relevance of the proposed frameworks for nonlinear regression and risk-aware prediction in real-world housing price modeling.