扰动导数：在Bregman损失下机器学习模型的无模型评估中的野重拟合
Perturbing the Derivative: Wild Refitting for Model-Free Evaluation of Machine Learning Models under Bregman Losses
AI总结：
通过野重拟合方法，在Bregman损失下实现对复杂机器学习模型的无模型超额风险评估。
摘要：
我们研究了经典惩罚经验风险最小化（ERM）在Bregman损失下的超额风险评估。我们证明，通过利用“野重拟合”的想法，可以高效地通过所谓的“野乐观”来上界超额风险，而不需要依赖于底层函数类的全局结构。这一性质使我们的方法本质上是无模型的。与传统分析不同，我们的框架仅使用一个数据集和对训练过程的黑盒访问。该方法涉及随机Rademacher对称化和通过在导数空间中进行适当缩放的扰动构造人工修改的输出，然后重新训练一个第二预测器以进行超额风险估计。我们建立了在固定设计设置下的高概率性能保证，证明在Bregman损失下，通过适当选择的野噪声尺度，野重拟合能够产生超额风险的有效上界。因此，我们的工作对于理论评估现代不透明的ML模型，如深度神经网络和生成模型，具有前景，因为在这些情况下，函数类过于复杂，无法用经典学习理论和经验过程技术来处理。
英文摘要：
We study the excess risk evaluation of classical penalized empirical risk minimization (ERM) with Bregman losses. We show that by leveraging the idea of wild refitting, one can efficiently upper bound the excess risk through the so-called "wild optimism," without relying on the global structure of the underlying function class. This property makes our approach inherently model-free. Unlike conventional analysis, our framework operates with just one dataset and black-box access to the training procedure. The method involves randomized Rademacher symmetrization and constructing artificially modified outputs by perturbation in the derivative space with appropriate scaling, upon which we retrain a second predictor for excess risk estimation. We establish high-probability performance guarantee under the fixed design setting, demonstrating that wild refitting under Bregman losses, with an appropriately chosen wild noise scale, yields a valid upper bound on the excess risk. Thus, our work is promising for theoretically evaluating modern opaque ML models, such as deep neural networks and generative models, where the function class is too complex for classical learning theory and empirical process techniques.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
