On Gradient-like Explanation under a Black-box Setting: When Black-box Explanations Become as Good as White-box

Attribution methods shed light on the explainability of data-driven approaches such as deep learning models by revealing the most contributing features to decisions that have been made. A widely accepted way of deriving feature attributions is to analyze the gradients of the target function with respect to input features. Analysis of gradients requires full access to the target system, meaning that solutions of this kind treat the target system as a white-box. However, the white-box assumption may be untenable due to security and safety concerns, thus limiting their practical applications. As an answer to the limited flexibility, this paper presents GEEX (gradient-estimation-based explanation), an explanation method that delivers gradient-like explanations under a black-box setting. Furthermore, we integrate the proposed method with a path method. The resulting approach iGEEX (integrated GEEX) satisfies the four fundamental axioms of attribution methods: sensitivity, insensitivity, implementation invariance, and linearity. With a focus on image data, the exhaustive experiments empirically show that the proposed methods outperform state-of-the-art black-box methods and achieve competitive performance compared to the ones with full access.