Bounding the Fairness of a Classifier Using Population-level Statistics

Abstract

Background: Classifiers increasingly affect people’s lives, necessitating their audit for fairness and accuracy on diverse populations. However, direct auditing is often not possible, due to a lack of access to the classifier or to suitable individual-level validation data. Objectives: This work aims to assess the fairness and accuracy of black-box classifiers using only population-level statistics, without requiring access to the classifier or individual predictions. Specifically, it introduces a method to lower-bound the discrepancy of a classifier: a quantity that jointly captures inaccuracy and unfairness. Methods: We define a novel measure of unfairness based on the equalized odds fairness criterion, quantifying the fraction of the population on which a classifier deviates from ideal fair behavior. Using this measure, we develop a computationally efficient procedure for calculating the tightest possible lower bound on the classifier’s discrepancy, using only aggregated rates of positive predictions and true positives across protected sub-populations. Results: Empirical evaluations confirm the tightness of the proposed lower bound in practical settings. The method is demonstrated on several use cases, including estimating the reliability of voting polls and assessing the fairness of patient identification from internet search data. The code and data are available at https://github.com/sivansabato/bfa2. Conclusions: This work provides a practical and interpretable framework for auditing classifiers using population-level statistics. The proposed approach enables stakeholders to identify fairness and accuracy concerns in settings where traditional auditing is not feasible.