Watermarking Counterfactual Explanations

The field of Explainable Artificial Intelligence (XAI) focuses on techniques for providing explanations to end-users about the decision-making processes that underlie modern-day machine learning (ML) models. Within the vast universe of XAI techniques, counterfactual (CF) explanations are often preferred by end-users as they help explain the predictions of ML models by providing an easy-to-understand in particular, malicious adversaries can exploit CF explanations to perform query-efficient model extraction attacks on proprietary ML models. In this paper, we propose a model-agnostic watermarking framework (for adding watermarks to CF explanations) that can be leveraged to detect unauthorized model extraction attacks (which rely on the watermarked CF explanations). Our novel framework solves a bi-level optimization problem to embed an indistinguishable watermark into the generated CF explanation such that any future model extraction attacks that rely on these watermarked CF explanations can be detected using a null hypothesis significance testing (NHST) scheme, while ensuring that these embedded watermarks do not compromise the quality of the generated CF explanations. We evaluate this framework's performance across a diverse set of real-world datasets, CF explanation methods, and model extraction techniques, and show that our watermarking detection system can be used to accurately identify extracted ML models that are trained using the watermarked CF explanations. Our work paves the way for the secure adoption of CF explanations in real-world applications.