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

2025-10-07

AI Summary

This work addresses the challenge of attributing high-order feature interactions—such as second- and higher-order joint contributions—in machine learning models. Methodologically, it generalizes Integrated Gradients to multidimensional tensor spaces, integrating statistical sufficiency conditions with chain complex structures from topological signal processing to rigorously define and derive high-order attribution operators satisfying uniqueness, symmetry, and conservation properties. Theoretically, it establishes, for the first time, a unified and provably sound mathematical foundation for high-order attribution, uncovering deep connections among explainable AI, statistical interaction effects, and topological data analysis. Empirically, the proposed framework demonstrates significant improvements in identifying nonlinear interactions and maintaining explanation consistency across multiple benchmark tasks.

Technology Category

• Machine Learning: Other Foundations of Machine Learning
• Computer Vision: Interpretability, Explainability, and Transparency
• Humans and AI: Explainable AI (XAI) for Human Understanding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 becomes less direct 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.

Problem

• Extends feature attribution to handle complex feature interactions
• Bridges explainable AI with statistics and topological signal processing
• Develops higher-order attribution theory based on Integrated Gradients

Innovation

• Develops higher-order feature attribution theory
• Extends Integrated Gradients foundation
• Connects statistics with topological signal processing