Nonlinear Axiomatic Attribution for Cooperative Games

Weida Li, Zhuanghua Liu, Yaoliang Yu, Bryan Kian Hsiang Low
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:3581-3603, 2026.

Abstract

The {Shapley} value is a widely used concept in attribution problems, as it uniquely satisfies the axioms of linearity, consistency, equal treatment, and efficiency. Often, the inclusion AUC metric is used to evaluate the quality of player rankings, in order to identify positively participating players. However, it can be established that the {Shapley} value is not always reliable for this purpose. The core issue lies in its linearity: the {Shapley} value acts as a linear operator with an excessively large null space, which is likely to contain non-negligible perturbations that remain indistinguishable to the operator. To address this limitation, we explore the design of nonlinear axiomatic attribution methods. Inspired by the least core, which is a popular nonlinear substitute for the {Shapley} value, we introduce a class of nonlinear attribution methods that retain the remaining necessary axioms. Each method yields a contribution vector that is the unique optimal solution to a minimization problem, which aims to approximate utility functions as faithfully as possible. In terms of the inclusion AUC metric, our experiments demonstrate the potential effectiveness of these methods compared to {Shapley} value variants that relax only the efficiency axiom.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-li26c, title = {Nonlinear Axiomatic Attribution for Cooperative Games}, author = {Li, Weida and Liu, Zhuanghua and Yu, Yaoliang and Low, Bryan Kian Hsiang}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {3581--3603}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26c/li26c.pdf}, url = {https://proceedings.mlr.press/v337/li26c.html}, abstract = {The {Shapley} value is a widely used concept in attribution problems, as it uniquely satisfies the axioms of linearity, consistency, equal treatment, and efficiency. Often, the inclusion AUC metric is used to evaluate the quality of player rankings, in order to identify positively participating players. However, it can be established that the {Shapley} value is not always reliable for this purpose. The core issue lies in its linearity: the {Shapley} value acts as a linear operator with an excessively large null space, which is likely to contain non-negligible perturbations that remain indistinguishable to the operator. To address this limitation, we explore the design of nonlinear axiomatic attribution methods. Inspired by the least core, which is a popular nonlinear substitute for the {Shapley} value, we introduce a class of nonlinear attribution methods that retain the remaining necessary axioms. Each method yields a contribution vector that is the unique optimal solution to a minimization problem, which aims to approximate utility functions as faithfully as possible. In terms of the inclusion AUC metric, our experiments demonstrate the potential effectiveness of these methods compared to {Shapley} value variants that relax only the efficiency axiom.} }
Endnote
%0 Conference Paper %T Nonlinear Axiomatic Attribution for Cooperative Games %A Weida Li %A Zhuanghua Liu %A Yaoliang Yu %A Bryan Kian Hsiang Low %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-li26c %I PMLR %P 3581--3603 %U https://proceedings.mlr.press/v337/li26c.html %V 337 %X The {Shapley} value is a widely used concept in attribution problems, as it uniquely satisfies the axioms of linearity, consistency, equal treatment, and efficiency. Often, the inclusion AUC metric is used to evaluate the quality of player rankings, in order to identify positively participating players. However, it can be established that the {Shapley} value is not always reliable for this purpose. The core issue lies in its linearity: the {Shapley} value acts as a linear operator with an excessively large null space, which is likely to contain non-negligible perturbations that remain indistinguishable to the operator. To address this limitation, we explore the design of nonlinear axiomatic attribution methods. Inspired by the least core, which is a popular nonlinear substitute for the {Shapley} value, we introduce a class of nonlinear attribution methods that retain the remaining necessary axioms. Each method yields a contribution vector that is the unique optimal solution to a minimization problem, which aims to approximate utility functions as faithfully as possible. In terms of the inclusion AUC metric, our experiments demonstrate the potential effectiveness of these methods compared to {Shapley} value variants that relax only the efficiency axiom.
APA
Li, W., Liu, Z., Yu, Y. & Low, B.K.H.. (2026). Nonlinear Axiomatic Attribution for Cooperative Games. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:3581-3603 Available from https://proceedings.mlr.press/v337/li26c.html.

Related Material