Beyond additivity: sparse isotonic shapley regression toward nonlinear explainability
摘要
Shapley values, a gold standard for feature attribution in Explainable AI, face two primary challenges. First, the canonical Shapley framework assumes that the worth function is additive, yet real-world payoff constructions—driven by non-Gaussian distributions, heavy tails, feature dependence, or domain-specific loss scales—often violate this assumption, leading to distorted attributions. Second, achieving sparse explanations in high-dimensional settings by computing dense Shapley values and then applying ad hoc thresholding is prohibitively costly and risks inconsistency. We introduce Sparse Isotonic Shapley Regression (SISR), a unified nonlinear explanation framework. SISR simultaneously learns a monotonic transformation to restore additivity—obviating the need for a closed-form specification—and enforces an L0 sparsity constraint on the Shapley vector, enhancing computational efficiency in large feature spaces. Its optimization algorithm leverages Pool-Adjacent-Violators for efficient isotonic regression and normalized hard-thresholding for support selection, ensuring ease in implementation and global convergence guarantees. Analysis shows that SISR recovers the true transformation in a wide range of scenarios and achieves strong support recovery even in high noise. Moreover, we are the first to demonstrate that irrelevant features and inter-feature dependencies can induce a true payoff transformation that deviates substantially from linearity. Extensive experiments in regression, logistic regression, and tree ensembles demonstrate that SISR stabilizes attributions across payoff schemes and correctly filters irrelevant features; in contrast, standard Shapley values suffer severe rank and sign distortions. By unifying nonlinear transformation estimation with sparsity pursuit, SISR advances the frontier of nonlinear explainability, providing a theoretically grounded and practical attribution framework.