A Mathematical Framework for Integrating Neural Networks into Stochastic DEA Models to Reduce Variance and Improve Prediction Stability

Abstract

This study proposes a novel mathematical framework that integrates neural networks into Stochastic Data Envelopment Analysis (SDEA) to reduce variance and enhance the stability of efficiency prediction under uncertainty. Traditional DEA models rely on linear or piecewise-linear frontiers and are highly sensitive to noise, resulting in unstable efficiency scores and unreliable rankings. The proposed hybrid framework addresses these limitations by combining stochastic frontier modeling, noise-distribution assumptions, and neural network function approximation to construct a smooth, flexible, and noise-resilient efficiency frontier. Neural components capture nonlinear relationships among inputs and outputs, while regularization and bootstrapping techniques stabilize estimation and mitigate variance inflation. Empirical experiments demonstrate that the integrated model outperforms classical DEA, stochastic DEA, and bootstrap-corrected DEA in terms of variance reduction, robustness to noise, and stability across repeated sampling. Efficiency scores exhibit narrower confidence intervals, more consistent DMU rankings, and improved frontier curvature representation. Sensitivity analyses further show that the model remains robust under different noise structures and hyperparameter settings. The findings highlight the potential of combining machine learning with stochastic optimization to advance the methodological foundation of DEA. By enhancing frontier flexibility and reducing noise-induced bias, the proposed framework provides a more reliable tool for efficiency evaluation in complex and uncertain production environments. Future work should focus on enhancing interpretability, reducing computational cost, and relaxing distributional assumptions to further extend the applicability of this hybrid approach.