Optimized Score Transformation for Fair Classification

Recent years have seen a surge of interest in the problem of fair classification, which is concerned with disparities in classification output or performance when conditioned on a protected attribute such as race or gender, or ethnicity. Many measures of fairness have been introduced [1-14] and fairness-enhancing interventions have been proposed to mitigate these disparities [15]. Roughly categorized, these interventions either (i) change data used to train a classifier (pre-processing) [16-20], (ii) change a classifier's output (post-processing) [4, 21-24], or (iii) directly change a classification model to ensure fairness (in-processing) [5, 25-32]. This paper places more emphasis on probabilistic classification in which the outputs of interest are predicted probabilities of belonging to one of the classes, often referred to as scores, as opposed to binary predictions. Scores are desirable because they indicate confidences in predictions. We propose an optimization formulation for transforming scores to satisfy fairness constraints while minimizing the loss in utility. The formulation accommodates any fairness criteria that can be expressed as linear inequalities involving conditional means of scores, including variants of statistical parity (SP) [1] and equalized odds (EO) [4, 5]. We derive a closed-form expression for the optimal transformed scores and a convex dual optimization problem for the Lagrange multipliers that parametrize the transformation.