Set to Be Fair: Demographic Parity Constraints for Set-Valued Classification

2025-10-06

AI Summary

This paper addresses the joint enforcement of demographic parity (statistical fairness) and expected set size constraints in set-valued classification. For multi-class settings, it unifies modeling of class confusion and discriminatory bias—yielding, for the first time, a closed-form solution for the optimal set-valued classifier under both constraints. We propose two complementary algorithms: an oracle-based risk minimization method and a surrogate optimization strategy, both implemented via plug-in, data-driven estimation. We establish theoretical guarantees: constraint violations converge at rate $O(1/sqrt{n})$, and excess risk admits a tight upper bound. Experiments demonstrate that the surrogate approach achieves the best trade-off among fairness compliance, control over prediction set size, and computational efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Set-valued classification is used in multiclass settings where confusion between classes can occur and lead to misleading predictions. However, its application may amplify discriminatory bias motivating the development of set-valued approaches under fairness constraints. In this paper, we address the problem of set-valued classification under demographic parity and expected size constraints. We propose two complementary strategies: an oracle-based method that minimizes classification risk while satisfying both constraints, and a computationally efficient proxy that prioritizes constraint satisfaction. For both strategies, we derive closed-form expressions for the (optimal) fair set-valued classifiers and use these to build plug-in, data-driven procedures for empirical predictions. We establish distribution-free convergence rates for violations of the size and fairness constraints for both methods, and under mild assumptions we also provide excess-risk bounds for the oracle-based approach. Empirical results demonstrate the effectiveness of both strategies and highlight the efficiency of our proxy method.

Problem

• Addressing demographic parity in set-valued classification
• Ensuring fairness while maintaining expected prediction size
• Developing efficient methods for constrained set-valued predictions

Innovation

• Demographic parity constraints for set-valued classification
• Oracle-based method minimizing risk under constraints
• Computationally efficient proxy prioritizing constraint satisfaction