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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.02673 |
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| _version_ | 1866912939309531136 |
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| author | Ferrere, Baptiste Bousquet, Nicolas Gamboa, Fabrice Loubes, Jean-Michel Muré, Joseph |
| author_facet | Ferrere, Baptiste Bousquet, Nicolas Gamboa, Fabrice Loubes, Jean-Michel Muré, Joseph |
| contents | Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP values, and serves as a cornerstone of additive explainability. However, the lack of an explicit closed-form expression for general dependent distributions has forced practitioners to rely on costly sampling-based approximations. We completely resolve this limitation for categorical inputs. By bridging functional analysis with the extension of discrete Fourier analysis, we derive a closed-form decomposition without any assumption. Our formulation is computationally very efficient. It seamlessly recovers the classical independent case and extends to arbitrary dependence structures, including distributions with non-rectangular support. Furthermore, leveraging the intrinsic link between SHAP and ANOVA under independence, our framework yields a natural generalization of SHAP values for the general categorical setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02673 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Functional ANOVA Decomposition for Categorical Inputs Models Ferrere, Baptiste Bousquet, Nicolas Gamboa, Fabrice Loubes, Jean-Michel Muré, Joseph Machine Learning Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP values, and serves as a cornerstone of additive explainability. However, the lack of an explicit closed-form expression for general dependent distributions has forced practitioners to rely on costly sampling-based approximations. We completely resolve this limitation for categorical inputs. By bridging functional analysis with the extension of discrete Fourier analysis, we derive a closed-form decomposition without any assumption. Our formulation is computationally very efficient. It seamlessly recovers the classical independent case and extends to arbitrary dependence structures, including distributions with non-rectangular support. Furthermore, leveraging the intrinsic link between SHAP and ANOVA under independence, our framework yields a natural generalization of SHAP values for the general categorical setting. |
| title | Exact Functional ANOVA Decomposition for Categorical Inputs Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.02673 |