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arXiv · 2603.02673

Exact Functional ANOVA Decomposition for Categorical Inputs Models

Baptiste Ferrere·Nicolas Bousquet·Fabrice Gamboa·Jean-Michel Loubes·Joseph Muré
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Abstract

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.

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Baptiste Ferrere, Nicolas Bousquet, Fabrice Gamboa, Jean-Michel Loubes, Joseph Muré. 2026-06-09. Exact Functional ANOVA Decomposition for Categorical Inputs Models. https://arxiv.org/abs/2603.02673

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