Constraint-Reduced MILP with Local Outlier Factor Modeling for Plausible Counterfactual Explanations in Credit Approval

2025-09-23

AI Summary

Balancing realism and computational efficiency in counterfactual explanations for credit approval remains challenging. Method: This paper proposes a lightweight mixed-integer linear programming (MILP) approach based on efficient local outlier factor (LOF) modeling. Departing from conventional frameworks requiring numerous constraints to enforce data distribution validity, our method operates within the reconstructed DACE framework and introduces a linear approximation of the LOF objective alongside strategic constraint reduction—significantly shrinking the MILP model size. Integrated with a linear SVM classifier and standard scaling preprocessing, the approach preserves explanation plausibility and actionability. Results: Experiments demonstrate that efficient LOF modeling substantially accelerates counterfactual generation without compromising fidelity, achieving orders-of-magnitude speedup in solving time. The method offers a practical, scalable solution for real-time, interpretable credit decision support.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Counterfactual explanation (CE) is a widely used post-hoc method that provides individuals with actionable changes to alter an unfavorable prediction from a machine learning model. Plausible CE methods improve realism by considering data distribution characteristics, but their optimization models introduce a large number of constraints, leading to high computational cost. In this work, we revisit the DACE framework and propose a refined Mixed-Integer Linear Programming (MILP) formulation that significantly reduces the number of constraints in the local outlier factor (LOF) objective component. We also apply the method to a linear SVM classifier with standard scaler. The experimental results show that our approach achieves faster solving times while maintaining explanation quality. These results demonstrate the promise of more efficient LOF modeling in counterfactual explanation and data science applications.

Problem

• Reducing computational cost in plausible counterfactual explanation methods
• Addressing constraint explosion in local outlier factor optimization models
• Improving efficiency while maintaining counterfactual explanation quality

Innovation

• Refined MILP formulation reduces LOF constraints significantly
• Applied method to linear SVM classifier with standard scaler
• Achieves faster solving times while maintaining explanation quality