Logic-based Explanations for Linear Support Vector Classifiers with Reject Option

TL;DR

The paper tackles explainability for linear SVCs with a reject option by encoding the classifier and its rejection mechanism as quantifier-free first-order formulas over linear real arithmetic and solving entailment with a linear program (LP) solver. It provides a method to compute minimal, provably correct explanations for individual instances, leveraging Algorithm 1 to iteratively prune features while preserving the predicted class, including rejection. Empirical results on six datasets show the approach yields up to $\;286\times$ faster explanations and often smaller explanations than Anchors, demonstrating strong efficiency gains and maintained correctness. The work offers a scalable, trustworthy XAI framework for reject-option classifiers and can be extended to other models and non-linear variants.

Abstract

Support Vector Classifier (SVC) is a well-known Machine Learning (ML) model for linear classification problems. It can be used in conjunction with a reject option strategy to reject instances that are hard to correctly classify and delegate them to a specialist. This further increases the confidence of the model. Given this, obtaining an explanation of the cause of rejection is important to not blindly trust the obtained results. While most of the related work has developed means to give such explanations for machine learning models, to the best of our knowledge none have done so for when reject option is present. We propose a logic-based approach with formal guarantees on the correctness and minimality of explanations for linear SVCs with reject option. We evaluate our approach by comparing it to Anchors, which is a heuristic algorithm for generating explanations. Obtained results show that our proposed method gives shorter explanations with reduced time cost.

Figures (1)

• Figure 1: Classification through features $f_{1}$ and $f_{2}$.