Optimized Score Transformation for Fair Classification
Optimized Score Transformation for Fair Classification
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发表时间：
2019-05
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通讯作者：
Dennis Wei;K. Ramamurthy;F. Calmon
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作者：
Dennis Wei;K. Ramamurthy;F. Calmon
本文考虑公平的概率分类，其中主要兴趣的输出是预测概率，通常称为分数。我们制定的问题，转换分数，以满足公平性的约束，是线性的条件平均分数，同时最大限度地减少效用损失。该公式可以应用于后处理分类器输出或预处理训练数据，从而允许在选择分类算法时的最大自由度。我们推导出一个封闭形式的表达的最佳转换的分数和凸优化问题的转换参数。在总体极限下，变换后的得分函数是关于最优无约束得分的交叉熵的公平约束最小值。在有限样本设置中，我们建议使用标准概率分类器和ADMM的组合来接近这个解决方案。从有限样本过程中得到的变换参数是渐近最优的。综合实验比较10个现有的方法表明，所提出的FairScoreTransformer具有优势的分数为基础的指标，如Brier分数和AUC，同时保持竞争力的二进制标记为基础的指标，如准确性。
This paper considers fair probabilistic 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 the loss in utility. The formulation can be applied either to post-process classifier outputs or to pre-process training data, 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 optimal unconstrained scores. In the finite sample setting, we propose to approach this solution using a combination of standard probabilistic classifiers and ADMM. The transformation parameters obtained from the finite-sample procedure are shown to be asymptotically optimal. Comprehensive experiments comparing to 10 existing methods show that the proposed FairScoreTransformer has advantages for score-based metrics such as Brier score and AUC while remaining competitive for binary label-based metrics such as accuracy.