Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures

2025-03-11

AI Summary

This work addresses the fragmentation issue of counterfactual explanations in model ensembles. We propose the first unified counterfactual generation method explicitly designed for multi-model joint constraints. Our core contribution is the novel integration of entropy-based risk measures into counterfactual optimization, establishing a tunable risk-parameterized constraint framework that enables continuous trade-offs between *ensemble-wide validity* and *low feature modification cost*—reducing to worst-case robust solutions at extremal parameter values. To ensure transferability across constituent models, we combine gradient-driven search with ensemble feasibility modeling. Extensive evaluation on real-world datasets demonstrates that our approach reduces average feature modification cost by 18% compared to state-of-the-art baselines, while maintaining validity across 70%–100% of ensemble models. This significantly improves explanation consistency and practical utility in ensemble settings.

Technology Category

• Machine Learning: Ensemble Methods
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Counterfactual explanations indicate the smallest change in input that can translate to a different outcome for a machine learning model. Counterfactuals have generated immense interest in high-stakes applications such as finance, education, hiring, etc. In several use-cases, the decision-making process often relies on an ensemble of models rather than just one. Despite significant research on counterfactuals for one model, the problem of generating a single counterfactual explanation for an ensemble of models has received limited interest. Each individual model might lead to a different counterfactual, whereas trying to find a counterfactual accepted by all models might significantly increase cost (effort). We propose a novel strategy to find the counterfactual for an ensemble of models using the perspective of entropic risk measure. Entropic risk is a convex risk measure that satisfies several desirable properties. We incorporate our proposed risk measure into a novel constrained optimization to generate counterfactuals for ensembles that stay valid for several models. The main significance of our measure is that it provides a knob that allows for the generation of counterfactuals that stay valid under an adjustable fraction of the models. We also show that a limiting case of our entropic-risk-based strategy yields a counterfactual valid for all models in the ensemble (worst-case min-max approach). We study the trade-off between the cost (effort) for the counterfactual and its validity for an ensemble by varying degrees of risk aversion, as determined by our risk parameter knob. We validate our performance on real-world datasets.

Problem

• Generating counterfactual explanations for model ensembles.
• Addressing the challenge of single counterfactual for multiple models.
• Using entropic risk measures to optimize counterfactual validity.

Innovation

• Uses entropic risk measures for counterfactual explanations
• Generates counterfactuals valid for multiple ensemble models
• Adjustable risk parameter controls counterfactual validity