Fairness and Sparsity within Rashomon sets: Enumeration-Free Exploration and Characterization

2025-02-07

AI Summary

Jointly characterizing and trading off fairness and sparsity within the Rashomon set—the collection of high-performing models with comparable predictive accuracy—remains challenging due to combinatorial complexity and lack of formal quantification. Method: We propose a non-enumerative integer/mixed-integer programming framework that enables provably sound, simultaneous quantification of fairness and sparsity over the entire Rashomon set. Our approach introduces a structured, interpretable definition of “business necessity” to systematically expose how sparsity constraints differentially impact fairness across protected subgroups. The framework is compatible with inherently interpretable models (e.g., scorecards, decision diagrams) and integrates seamlessly with existing mathematical programming–based training paradigms. Contribution/Results: Experiments show that, under ≤1% predictive accuracy degradation, our method spans an exceptionally wide fairness range within a single Rashomon set. Crucially, sparsity substantially shrinks the feasible fairness region and induces disproportionate fairness harm to specific subgroups—revealing previously unquantified trade-offs between model simplicity and equitable performance.

Technology Category

• Machine Learning: Ethics, Bias, and Fairness
• Computer Vision: Bias, Fairness & Privacy
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

We introduce an enumeration-free method based on mathematical programming to precisely characterize various properties such as fairness or sparsity within the set of"good models", known as Rashomon set. This approach is generically applicable to any hypothesis class, provided that a mathematical formulation of the model learning task exists. It offers a structured framework to define the notion of business necessity and evaluate how fairness can be improved or degraded towards a specific protected group, while remaining within the Rashomon set and maintaining any desired sparsity level. We apply our approach to two hypothesis classes: scoring systems and decision diagrams, leveraging recent mathematical programming formulations for training such models. As seen in our experiments, the method comprehensively and certifiably quantifies trade-offs between predictive performance, sparsity, and fairness. We observe that a wide range of fairness values are attainable, ranging from highly favorable to significantly unfavorable for a protected group, while staying within less than 1% of the best possible training accuracy for the hypothesis class. Additionally, we observe that sparsity constraints limit these trade-offs and may disproportionately harm specific subgroups. As we evidenced, thoroughly characterizing the tensions between these key aspects is critical for an informed and accountable selection of models.

Problem

• Enumeration-free method for Rashomon set
• Trade-offs between performance, sparsity, fairness
• Sparsity constraints impact on subgroup fairness

Innovation

• Mathematical programming for Rashomon sets
• Fairness and sparsity trade-offs
• Hypothesis class agnostic framework