Beyond Additivity: Sparse Isotonic Shapley Regression toward Nonlinear Explainability

TL;DR

This paper introduces Sparse Isotonic Shapley Regression (SISR), a novel method that improves feature attribution in Explainable AI by modeling nonlinear transformations and enforcing sparsity, leading to more accurate and stable explanations in complex, high-dimensional settings.

Contribution

SISR unifies nonlinear transformation learning with sparsity constraints, providing a computationally efficient, theoretically grounded framework for more accurate feature attributions in non-additive, high-dimensional data.

Findings

SISR accurately recovers true feature transformations across various scenarios.

It effectively filters irrelevant features and maintains stable attributions.

Standard Shapley values suffer from distortions under complex payoff structures.

Abstract

Shapley values, a gold standard for feature attribution in Explainable AI, face two key 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 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 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.