Fair Decisions from Calibrated Scores: Achieving Optimal Classification While Satisfying Sufficiency
This work provides an exact solution for optimal classification under sufficiency, a critical fairness constraint, for researchers and practitioners working on fair machine learning.
This paper addresses the challenge of achieving optimal binary classification while satisfying the sufficiency fairness constraint, which is often violated even by perfectly group-calibrated scores. The authors provide an exact solution for optimal randomized classification under sufficiency for finite sets of group-calibrated scores, and they also identify a classifier that minimizes deviation from separation while satisfying sufficiency.
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.