xNN-SF: An Explainable Neural Network Inspired by Stochastic Frontier Model

Neural networks have emerged as a strong competitor to traditional regression and statistical models. Although neural networks exhibit strong predictive performance, they lack model interpretability. In this paper, we propose an explainable neural network inspired by stochastic frontier model (xNN-SF) aiming to illuminate the black box and strike a balance between prediction accuracy and model interpretability. Precisely, the input features are projected into three directions and then fed into three neural subnetworks. Each subnetwork extracts a different influence: the main influence, the negative influence, and the variance perturbation. To promote interpretability, the former two subnetworks are constrained to be monotonic. Unlike the other two, the third subsystem comprises an ensemble of multiple interlaced neural networks rather than a solitary one, with each constituent net sequentially trained via a boosting procedure. The outputs are obtained by weighting the results from the three subnetworks. We develop a simple implementation procedure and evaluate our proposed methodology against multiple benchmarks across various real-world datasets. The results demonstrate that our model maintains competitive prediction performance while also enhancing interpretability.