# Beyond Additivity: Sparse Isotonic Shapley Regression toward Nonlinear Explainability

arXiv: https://arxiv.org/abs/2512.03112 · HTML: https://mlsanity.com/paper/2512.03112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation](https://mlsanity.com/paper/1903.10992/) (2019)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Shapley values for feature selection: The good, the bad, and the axioms](https://mlsanity.com/paper/2102.10936/) (2021)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [The Grammar of Interactive Explanatory Model Analysis](https://mlsanity.com/paper/2005.00497/) (2020)
- [Predictive and Causal Implications of using Shapley Value for Model Interpretation](https://mlsanity.com/paper/2008.05052/) (2020)
- [Grouped Feature Importance and Combined Features Effect Plot](https://mlsanity.com/paper/2104.11688/) (2021)
- [Derivative-based Shapley value for global sensitivity analysis and machine learning explainability](https://mlsanity.com/paper/2303.15183/) (2023)

## Abstract (arXiv)

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.