Higher-Order Feature Attribution: Bridging Statistics, Explainable AI, and Topological Signal Processing

Feature attributions are post-training analysis methods that assess how various input features of a machine learning model contribute to an output prediction. Their interpretation is straightforward when features act independently, but it becomes less clear when the predictive model involves interactions, such as multiplicative relationships or joint feature contributions. In this work, we propose a general theory of higher-order feature attribution, which we develop on the foundation of Integrated Gradients (IG). This work extends existing frameworks in the literature on explainable AI. When using IG as the method of feature attribution, we discover natural connections to statistics and topological signal processing. We provide several theoretical results that establish the theory, and we validate our theory on a few examples.