Set to Be Fair: Demographic Parity Constraints for Set-Valued Classification
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916991393071104 |
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| author | Cohen, Eyal Denis, Christophe Hebiri, Mohamed |
| author_facet | Cohen, Eyal Denis, Christophe Hebiri, Mohamed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Set to Be Fair: Demographic Parity Constraints for Set-Valued Classification Cohen, Eyal Denis, Christophe Hebiri, Mohamed Machine Learning 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. |
| title | Set to Be Fair: Demographic Parity Constraints for Set-Valued Classification |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.04926 |