L2正则化能直接保证模型概率校准精度，无需额外校准步骤。
$L_2$-Regularized Empirical Risk Minimization Guarantees Small Smooth Calibration Error
- 用L2正则化优化直接控制平滑校准误差
- 理论证明在有限样本下误差受正则强度和复杂度约束
- 适用于核方法与逻辑回归，实验验证无需后处理
概率校准对可靠机器学习至关重要，但标准训练过程如何生成校准良好的模型仍不明确。本文首次从理论上证明，标准的L2正则化经验风险最小化可直接控制平滑校准误差（smCE），无需事后校准或专门设计的校准正则项。我们基于优化误差、正则强度和Rademacher复杂度，建立了smCE的有限样本泛化界，并将其应用于再生核希尔伯特空间中的模型，推导出核岭回归和逻辑回归的具体校准保证。实验验证了这些理论结果，表明L2正则化ERM可在无需提升或事后校准的情况下实现良好校准。所有实验代码已公开于https://github.com/msfuji0211/erm_calibration。
原文摘要 · Abstract (English)
Calibration of predicted probabilities is critical for reliable machine learning, yet it is poorly understood how standard training procedures yield well-calibrated models. This work provides the first theoretical proof that canonical $L_{2}$-regularized empirical risk minimization directly controls the smooth calibration error (smCE) without post-hoc correction or specialized calibration-promoting regularizer. We establish finite-sample generalization bounds for smCE based on optimization error, regularization strength, and the Rademacher complexity. We then instantiate this theory for models in reproducing kernel Hilbert spaces, deriving concrete guarantees for kernel ridge and logistic regression. Our experiments confirm these specific guarantees, demonstrating that $L_{2}$-regularized ERM can provide a well-calibrated model without boosting or post-hoc recalibration. The source code to reproduce all experiments is available at https://github.com/msfuji0211/erm_calibration.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。