Title: Error Analysis of Shapley Value-Based Model Explanations: An Informative Perspective

Abstract: Shapley value attribution is an increasingly popular explainable AI (XAI) method, which quantifies the contribution of each feature to the model's output. However, recent work has shown that most existing methods to implement Shapley value attributions have some drawbacks. Due to these drawbacks, the resulting Shapley value attributions may provide biased or unreliable explanations, which fail to correctly capture the true intrinsic relationships between features and model outputs. Moreover, it is difficult to evaluate these explanation errors because the true underlying dependencies between features and model outputs are typically unknown. In this paper, we theoretically analyze the explanation errors of Shapley value attributions by decomposing the explanation error into two components: observation bias and structural bias. We also clarify the underlying causes of these two biases and demonstrate that there is a trade-off between them. Based on this error analysis framework, we develop two novel concepts: over-informative and under-informative explanations. We theoretically analyze the potential over-informativeness and under-informativeness of existing Shapley value attribution methods. Particularly for the widely deployed assumption-based Shapley value attributions, we affirm that they can easily be under-informative due to the distribution drift caused by distributional assumptions. We also propose a measurement tool to quantify the distribution drift that causes such errors.