Attribution methods provide an insight into the decision-making process of machine learning models, especially deep neural networks, by assigning contribution scores to each individual feature. However, the attribution problem has not been well-defined, which lacks a unified guideline to the contribution assignment process. Furthermore, existing attribution methods often built upon various empirical intuitions and heuristics. There still lacks a general theoretical framework that not only can offer a good description of the attribution problem, but also can be applied to unifying and revisiting existing attribution methods. To bridge the gap, in this paper, we propose a Taylor attribution framework, which models the attribution problem as how to decide individual payoffs in a coalition. Then, we reformulate fourteen mainstream attribution methods into the Taylor framework and analyze these attribution methods in terms of rationale, fidelity, and limitation in the framework. Moreover, we establish three principles for a good attribution in the Taylor attribution framework, i.e., low approximation error, correct Taylor contribution assignment, and unbiased baseline selection. Finally, we empirically validate the Taylor reformulations and reveal a positive correlation between the attribution performance and the number of principles followed by the attribution method via benchmarking on real-world datasets.

Attribution methods have been developed to understand the decision making process of machine learning models, especially deep neural networks, by assigning importance scores to individual features. Existing attribution methods often built upon empirical intuitions and heuristics. There still lacks a unified framework that can provide deeper understandings of their rationales, theoretical fidelity, and limitations. To bridge the gap, we present a Taylor attribution framework to theoretically characterize the fidelity of explanations. The key idea is to decompose model behaviors into first-order, high-order independent, and high-order interactive terms, which makes clearer attribution of high-order effects and complex feature interactions. Three desired properties are proposed for Taylor attributions, i.e., low model approximation error, accurate assignment of independent and interactive effects. Moreover, several popular attribution methods are mathematically reformulated under the unified Taylor attribution framework. Our theoretical investigations indicate that these attribution methods implicitly reflect high-order terms involving complex feature interdependencies. Among these methods, Integrated Gradient is the only one satisfying the proposed three desired properties. New attribution methods are proposed based on Integrated Gradient by utilizing the Taylor framework. Experimental results show that the proposed method outperforms the existing ones in model interpretations.