针对相关特征的神经网络，提出两种自适应正则化方法提升预测性能。
Adaptive Norm-Based Regularization for Neural Networks
- 基于输入特征协方差结构改进权重衰减，实现依赖关系感知的正则化。
- 结合稀疏性与结构信息，使模型在高维数据下更稳定、泛化更好。
- 适用于特征相关或高维场景，如基因表达分析和建筑能耗预测。
本文研究神经网络中的范数正则化方法。比较现有惩罚策略后，提出两种扩展经典岭回归与套索型惩罚的新方法。第一种将输入特征的协方差结构引入岭型ℓ₂正则项，使正则化能反映特征依赖关系；第二种结合ℓ₁稀疏惩罚与协方差感知的ℓ₂正则，得到兼具稀疏性和结构信息的网络权重。通过蒙特卡洛模拟评估不同数据生成设定下的表现，并在建筑冷却负荷预测与高维基因表达数据的白血病细胞分类两个真实数据集上验证。结果表明，所提正则化方法在模拟与真实数据中均提升了未见数据的预测性能，且在特征相关或高维情形下比标准范数正则更有效控制模型复杂度。
原文摘要 · Abstract (English)
In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network models. The first strategy modifies weight decay by incorporating the covariance structure of the input features into a ridge-type $\ell_2$ penalty, allowing regularization to account for feature dependence. The second combines an $\ell_1$ sparsity penalty with covariance-aware $\ell_2$ regularization, producing neural network weights that are both sparse and structurally informed. Monte Carlo simulations are used to evaluate these methods under different data-generating settings, followed by two real-data applications on building cooling-load prediction and leukemia cell-type classification from high-dimensional gene expression data. Across simulated and real-data examples, the proposed regularizers improve predictive performance on unseen data and provide more effective complexity control than standard norm-based penalties, particularly when features are correlated or high-dimensional.
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