通过领域约束单调性提升深度模型泛化能力，减少过拟合。
DIM: Enforcing Domain-Informed Monotonicity in Deep Neural Networks
- 以线性基线为参照，惩罚偏离单调性的行为。
- 在芝加哥网约车数据集上提升预测性能，且对多种网络结构有效。
- 适合需可解释性与稳定趋势的领域，如经济、医疗建模。
深度学习模型虽在预测任务中表现优异，但因结构复杂、参数量大，常因过拟合而记忆训练数据中的噪声而非学习可泛化的模式。本文提出一种新正则化方法——领域约束单调性（DIM），通过在复杂深度神经网络中保持领域相关的单调关系来改进预测效果。具体而言，该方法基于线性基准评估单调性违反程度，并将偏差度量融入训练目标，以引导模型遵循预期趋势。我们通过芝加哥真实网约车数据集和合成数据集验证该方法，在多种神经网络架构下，即使施加较弱的单调性约束，模型性能仍持续提升。结果表明，通过引入领域知识约束的单调性正则化，能有效缓解过拟合并增强深度网络的预测能力。
原文摘要 · Abstract (English)
While deep learning models excel at predictive tasks, they often overfit due to their complex structure and large number of parameters, causing them to memorize training data, including noise, rather than learn patterns that generalize to new data. To tackle this challenge, this paper proposes a new regularization method, i.e., Enforcing Domain-Informed Monotonicity in Deep Neural Networks (DIM), which maintains domain-informed monotonic relationships in complex deep learning models to further improve predictions. Specifically, our method enforces monotonicity by penalizing violations relative to a linear baseline, effectively encouraging the model to follow expected trends while preserving its predictive power. We formalize this approach through a comprehensive mathematical framework that establishes a linear reference, measures deviations from monotonic behavior, and integrates these measurements into the training objective. We test and validate the proposed methodology using a real-world ridesourcing dataset from Chicago and a synthetically created dataset. Experiments across various neural network architectures show that even modest monotonicity constraints consistently enhance model performance. DIM enhances the predictive performance of deep neural networks by applying domain-informed monotonicity constraints to regularize model behavior and mitigate overfitting
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