To explain complex models based on their inputs, many feature attribution methods have been developed that assign importance scores to input features. However, some recent work challenges the robustness of feature attributions by showing that these methods are sensitive to input and model perturbations, while other work addresses this robustness issue by proposing robust attribution methods and model modifications. Nevertheless, previous work on attribution robustness has focused primarily on gradient-based feature attributions. In contrast, the robustness properties of removal-based attribution methods are not comprehensively well understood. To bridge this gap, we theoretically characterize the robustness of removal-based feature attributions. Specifically, we provide a unified analysis of such methods and prove upper bounds for the difference between intact and perturbed attributions, under settings of both input and model perturbations. Our empirical experiments on synthetic and real-world data validate our theoretical results and demonstrate their practical implications.

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