On Gradient-like Explanation under a Black-box Setting: When Black-box
  Explanations Become as Good as White-box
Yi Cai Gerhard Wunder
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.