标题： 可识别的凸-凹回归通过子梯度正则化最小二乘法 显示英文标题

标题： Identifiable Convex-Concave Regression via Sub-gradient Regularised Least Squares

摘要： 我们提出了一种新颖的非参数回归方法，该方法将复杂的输入输出关系建模为凸和凹成分的总和。 该方法-可识别的凸-凹非参数最小二乘法（ICCNLS）-将目标函数分解为加性的形状约束成分，每个成分通过子梯度约束的仿射函数表示。 为了解决凸-凹分解中固有的仿射模糊性，我们引入了全局统计正交性约束，确保残差与截距和输入变量不相关。 这强制分解的可识别性并提高了可解释性。 我们进一步在子梯度上引入L1、L2和弹性网络正则化，以增强泛化能力和促进结构稀疏性。 所提出的方法在合成和现实世界的数据集上进行了评估，包括医疗定价数据，并显示出比传统CNLS和凸函数之差（DC）回归方法更高的预测准确性和模型简洁性。 我们的结果表明，当与凸-凹结构和子梯度正则化结合时，统计可识别性可以产生适用于预测、基准测试和政策评估的可解释模型。 显示英文摘要

摘要： We propose a novel nonparametric regression method that models complex input-output relationships as the sum of convex and concave components. The method-Identifiable Convex-Concave Nonparametric Least Squares (ICCNLS)-decomposes the target function into additive shape-constrained components, each represented via sub-gradient-constrained affine functions. To address the affine ambiguity inherent in convex-concave decompositions, we introduce global statistical orthogonality constraints, ensuring that residuals are uncorrelated with both intercept and input variables. This enforces decomposition identifiability and improves interpretability. We further incorporate L1, L2 and elastic net regularisation on sub-gradients to enhance generalisation and promote structural sparsity. The proposed method is evaluated on synthetic and real-world datasets, including healthcare pricing data, and demonstrates improved predictive accuracy and model simplicity compared to conventional CNLS and difference-of-convex (DC) regression approaches. Our results show that statistical identifiability, when paired with convex-concave structure and sub-gradient regularisation, yields interpretable models suited for forecasting, benchmarking, and policy evaluation.