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

arXiv: https://arxiv.org/abs/2509.19504 · HTML: https://mlsanity.com/paper/2509.19504/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 4 of 4)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)

## Abstract (arXiv)

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.