Interval Abstractions for Robust Counterfactual Explanations

TL;DR

This paper introduces an interval abstraction method that provides provable robustness guarantees for counterfactual explanations in machine learning models, ensuring their validity under a wide range of model changes.

Contribution

The paper proposes a novel interval abstraction technique for parametric models, formalizes a new robustness notion called Δ-robustness, and develops algorithms to verify and generate robust counterfactual explanations.

Findings

The approach offers provable robustness guarantees for CEs under extensive model variations.

Empirical results demonstrate the effectiveness of the method on neural networks and logistic regression.

Benchmarking shows the superiority of the proposed algorithms in generating robust CEs.

Abstract

Counterfactual Explanations (CEs) have emerged as a major paradigm in explainable AI research, providing recourse recommendations for users affected by the decisions of machine learning models. However, CEs found by existing methods often become invalid when slight changes occur in the parameters of the model they were generated for. The literature lacks a way to provide exhaustive robustness guarantees for CEs under model changes, in that existing methods to improve CEs' robustness are mostly heuristic, and the robustness performances are evaluated empirically using only a limited number of retrained models. To bridge this gap, we propose a novel interval abstraction technique for parametric machine learning models, which allows us to obtain provable robustness guarantees for CEs under a possibly infinite set of plausible model changes $\Delta$. Based on this idea, we formalise a robustness notion for CEs, which we call $\Delta$-robustness, in both binary and multi-class classification settings. We present procedures to verify $\Delta$-robustness based on Mixed Integer Linear Programming, using which we further propose algorithms to generate CEs that are $\Delta$-robust. In an extensive empirical study involving neural networks and logistic regression models, we demonstrate the practical applicability of our approach. We discuss two strategies for determining the appropriate hyperparameters in our method, and we quantitatively benchmark CEs generated by eleven methods, highlighting the effectiveness of our algorithms in finding robust CEs.