Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory

Fabian Fumagalli, Maximilian Muschalik, Eyke Hüllermeier, Barbara Hammer, Julia Herbinger
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:5140-5148, 2025.

Abstract

Feature-based explanations, using perturbations or gradients, are a prevalent tool to understand decisions of black box machine learning models. Yet, differences between these methods still remain mostly unknown, which limits their applicability for practitioners. In this work, we introduce a unified framework for local and global feature-based explanations using two well-established concepts: functional ANOVA (fANOVA) from statistics, and the notion of value and interaction from cooperative game theory. We introduce three fANOVA decompositions that determine the influence of feature distributions, and use game-theoretic measures, such as the Shapley value and interactions, to specify the influence of higher-order interactions. Our framework combines these two dimensions to uncover similarities and differences between a wide range of explanation techniques for features and groups of features. We then empirically showcase the usefulness of our framework on synthetic and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-fumagalli25a, title = {Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory}, author = {Fumagalli, Fabian and Muschalik, Maximilian and H{\"u}llermeier, Eyke and Hammer, Barbara and Herbinger, Julia}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {5140--5148}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/fumagalli25a/fumagalli25a.pdf}, url = {https://proceedings.mlr.press/v258/fumagalli25a.html}, abstract = {Feature-based explanations, using perturbations or gradients, are a prevalent tool to understand decisions of black box machine learning models. Yet, differences between these methods still remain mostly unknown, which limits their applicability for practitioners. In this work, we introduce a unified framework for local and global feature-based explanations using two well-established concepts: functional ANOVA (fANOVA) from statistics, and the notion of value and interaction from cooperative game theory. We introduce three fANOVA decompositions that determine the influence of feature distributions, and use game-theoretic measures, such as the Shapley value and interactions, to specify the influence of higher-order interactions. Our framework combines these two dimensions to uncover similarities and differences between a wide range of explanation techniques for features and groups of features. We then empirically showcase the usefulness of our framework on synthetic and real-world datasets.} }
Endnote
%0 Conference Paper %T Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory %A Fabian Fumagalli %A Maximilian Muschalik %A Eyke Hüllermeier %A Barbara Hammer %A Julia Herbinger %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-fumagalli25a %I PMLR %P 5140--5148 %U https://proceedings.mlr.press/v258/fumagalli25a.html %V 258 %X Feature-based explanations, using perturbations or gradients, are a prevalent tool to understand decisions of black box machine learning models. Yet, differences between these methods still remain mostly unknown, which limits their applicability for practitioners. In this work, we introduce a unified framework for local and global feature-based explanations using two well-established concepts: functional ANOVA (fANOVA) from statistics, and the notion of value and interaction from cooperative game theory. We introduce three fANOVA decompositions that determine the influence of feature distributions, and use game-theoretic measures, such as the Shapley value and interactions, to specify the influence of higher-order interactions. Our framework combines these two dimensions to uncover similarities and differences between a wide range of explanation techniques for features and groups of features. We then empirically showcase the usefulness of our framework on synthetic and real-world datasets.
APA
Fumagalli, F., Muschalik, M., Hüllermeier, E., Hammer, B. & Herbinger, J.. (2025). Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:5140-5148 Available from https://proceedings.mlr.press/v258/fumagalli25a.html.

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