Optimized Score Transformation for Consistent Fair Classification
\nameDennis Wei \nameKarthikeyan Natesan Ramamurthy \addrIBM Research 1101 Kitchawan Road Yorktown Heights, NY 10598, USA \AND\nameFlavio P. Calmon \addrJohn A. Paulson School of Engineering and Applied Sciences Harvard University 150 Western Ave Allston, MA 02134, USA
Abstract
This paper considers fair probabilistic binary classification where the outputs of primary interest are predicted probabilities, commonly referred to as scores. We formulate the problem of transforming scores to satisfy fairness constraints that are linear in conditional means of scores while minimizing a cross-entropy objective. The formulation can be applied directly to post-process classifier outputs and we also explore a pre-processing extension, thus allowing maximum freedom in selecting a classification algorithm. We derive a closed-form expression for the optimal transformed scores and a convex optimization problem for the transformation parameters. In the population limit, the transformed score function is the fairness-constrained minimizer of cross-entropy with respect to the true conditional probability of the outcome. In the finite sample setting, we propose a method called $\mathsf{FairScoreTransformer}$ to approach this solution using a combination of standard probabilistic classifiers and ADMM. We provide several consistency and finite-sample guarantees for $\mathsf{FairScoreTransformer}$ , relating to the transformation parameters and transformed score function that
中文速览
公平机器学习领域长期关注如何消除分类器在种族、性别等敏感属性上的歧视，但大多数方法针对的是最终的二元判断（批准/拒绝），而忽视了更有价值的概率分数（scores）本身的公平性。本文提出一个名为 FairScoreTransformer（FST）的方法，将现有分类器输出的概率分数进行后处理变换，使其在满足以条件均值线性不等式表达的公平约束（涵盖统计均等 statistical parity 和机会均等 equalized odds 等常见准则）的同时，最小化交叉熵损失。研究者推导出最优变换的闭合解，并将对偶参数的求解转化为凸优化问题，利用 ADMM 算法高效求解，同时给出了有限样本下的一致性保证和误差界。在与 10 种现有方法的全面对比实验中，FST 在 Brier score、AUC 等基于概率分数的指标上取得了更优的公平性与准确性权衡，在准确率等二元指标上也保持竞争力，对于那些需要把概率输出直接交给下游决策者（如医疗风险评估、人工审核场景）的应用具有重要实用价值。
原文 arXiv:1906.00066;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1906.00066v3