Using Submodular Optimization to Approximate Minimum-Size Abductive Path Explanations for Tree-Based Models

Louenas Bounia

Keywords: Explainable AI (XAI) \and Minimum-Size Abductive Explanations \and Decision Trees \and Random Forests \and Submodular Optimization \and Constraint Programming

Abstract: One of the key challenges of Explainable Artificial Intelligence (XAI) is providing concise and understandable explanations for classification model predictions. An abductive explanation for a given instance is a minimal set of features that justify the prediction. These minimal explanations are valuable for their interpretability, as they eliminate redundant or irrelevant information. However, computing these explanations is difficult, even for simpler classifiers like decision trees. Finding a minimum-size abductive explanation in decision trees is an NP-complete problem, and this complexity extends to random forests for minimum-size majoritary reasons. In this work, we focus on finding minimal sets of features along the paths leading to the decision, called path-abductive explanations. We show that the problem of finding minimum-size path-abductive explanations in decision trees and minimum-size path-majoritary reasons in random forests is also NP-complete. To address this, we reformulate the problem as a submodular optimization task and propose a greedy algorithm with optimality guarantees. Our experiments demonstrate that this algorithm produces near-optimal explanations efficiently and offers a strong alternative for difficult instances, where exact methods based on SAT encodings are computationally expensive. This approach is especially useful in resource-limited environments where modern SAT solvers are not feasible.

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission687/Authors, auai.org/UAI/2025/Conference/Submission687/Reproducibility_Reviewers

Submission Number: 687