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arXiv 2602.07285cs.LG
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基于校准分数的公平决策:在满足充分性的同时实现最优分类

Fair Decisions from Calibrated Scores: Achieving Optimal Classification While Satisfying Sufficiency

School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel(计算机科学与工程学院,耶路撒冷希伯来大学,以色列);The Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem, Israel(理性研究基金会,耶路撒冷希伯来大学,以色列)

Etam Benger, Katrina Ligett

AI总结:

本文针对充分性公平约束下的二元分类问题,提出了一种基于分组校准分数的后处理算法,能够实现最优随机分类,并给出了可行正预测值与错误遗漏率对的几何刻画。

摘要:

基于预测概率(分数)的二元分类是监督机器学习中的基本任务。在无约束设置中,阈值化分数是贝叶斯最优的,但使用单一阈值通常会违反统计群体公平约束。在独立性(统计均等)和分离性(均等机会)下,当分数已经满足相应准则时,这种阈值化就足够了。然而,这并不扩展到充分性:即使完全分组校准的分数——包括真实类别概率——在阈值化后也会违反预测均等。在这项工作中,我们提出了在充分性下最优二元(随机)分类的精确解,假设有限的分组校准分数集。我们给出了这些分类器可实现的正预测值(PPV)和错误遗漏率(FOR)可行对的几何刻画,并利用它推导出一个简单的后处理算法,该算法仅使用分组校准分数和组成员身份即可获得最优分类器。最后,由于充分性和分离性通常不兼容,我们确定了在满足充分性的前提下最小化与分离性偏差的分类器,并表明该分类器也可以通过我们的算法获得,其性能通常与最优值相当。

英文摘要:

Binary classification based on predicted probabilities (scores) is a fundamental task in supervised machine learning. While thresholding scores is Bayes-optimal in the unconstrained setting, using a single threshold generally violates statistical group fairness constraints. Under independence (statistical parity) and separation (equalized odds), such thresholding suffices when the scores already satisfy the corresponding criterion. However, this does not extend to sufficiency: even perfectly group-calibrated scores -- including true class probabilities -- violate predictive parity after thresholding. In this work, we present an exact solution for optimal binary (randomized) classification under sufficiency, assuming finite sets of group-calibrated scores. We provide a geometric characterization of the feasible pairs of positive predictive value (PPV) and false omission rate (FOR) achievable by such classifiers, and use it to derive a simple post-processing algorithm that attains the optimal classifier using only group-calibrated scores and group membership. Finally, since sufficiency and separation are generally incompatible, we identify the classifier that minimizes deviation from separation subject to sufficiency, and show that it can also be obtained by our algorithm, often achieving performance comparable to the optimum.

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。

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