用于多校准的增强特征提升

中文摘要 AI 辅助

多校准要求预测器的残差不仅在全球范围内无偏，而且在以预测器自身的水平集为条件并通过丰富的测试函数类重新加权后也无偏。在分布设置中，标准的提升方法通过反复离散化预测器的值域，然后审计并修复由此产生的水平集来实现这一点。一个后果是，在实践中，算法的保证对该舍入参数的参数化很敏感。因此，一个自然的理论问题是，如何进行无离散化的提升，从而在提升过程本身中避免这种舍入。在这里，我们分析了一种受Tax等人（2026）启发的替代性特征增强提升范式：在每一轮中，对将前一轮预测器的输出作为额外特征的假设调用平方损失预言机，并且仅对最终预测器进行舍入以使其具有有限个水平集，从而提供多校准保证。我们通过增强假设类的表达能力对该过程进行了理论分析，并展示了该类的表达能力如何产生一个保证层次结构，包括多准确性、多校准以及更强的水平集多校准概念。

英文摘要

Multicalibration requires a predictor's residuals to be unbiased not only globally, but also after conditioning on the predictor's own level sets and reweighting by a rich class of test functions. Standard boosting approaches in the distributional setting achieve this by repeatedly discretizing the predictor's range then auditing and repairing the resulting level sets. One consequence is that in practice, the algorithm's guarantees are sensitive to this parametrization of the rounding parameter. A natural theoretical question, then, is how to do discretization-free boosting which avoids this rounding within the boosting process itself. Here, we analyze an alternative feature-augmentation boosting paradigm inspired by Tax et al. (2026): at each round, a squared-loss oracle is called on hypotheses that receive the previous predictor's output as an additional feature, and only the final predictor is rounded to have a finite set of level sets to provide the multicalibration guarantee with respect to. We give a theoretical analysis of this procedure through the expressivity of the augmented hypothesis class, and show how the expressivity of this class yields a hierarchy of guarantees, including multiaccuracy, multicalibration, and the stronger notion of level-set multicalibration.

发表机构

• Cornell University（康奈尔大学）
• Ben-Gurion University of the Negev（内盖夫本-古里安大学）

机构由 AI 辅助整理，请以论文原文为准。