Researchers Develop Closed-Form Solution for Functional ANOVA Decomposition with Categorical Inputs
Researchers have published a method that provides an exact, closed-form functional ANOVA decomposition for machine learning models with categorical inputs under arbitrary dependence structures. Previously, practitioners had to rely on costly sampling-based approximations when input features were not independent. The work advances model interpretability by enabling efficient, exact decomposition of predictions into main effects and interactions, and generalizes SHAP values beyond the independence assumption.
A preprint posted to arXiv presents a theoretical framework that fully resolves a longstanding limitation in functional ANOVA for machine learning interpretability: the absence of a closed-form solution when input features are statistically dependent. The authors bridge functional analysis with discrete Fourier analysis to derive an exact decomposition applicable to categorical inputs under any dependence structure, including distributions with non-rectangular support. The method is computationally efficient and naturally recovers the classical independent-feature case as a special instance. Importantly, the framework also yields a generalization of SHAP values—a widely used tool for explaining model predictions—to the general categorical setting where features may be correlated. The paper was first submitted in March 2026 and revised in June 2026, suggesting ongoing refinement. By eliminating the need for sampling-based approximations, the approach could reduce computational costs and improve the reliability of explainability analyses in practice.
What's missing
The paper is a preprint and has not yet undergone formal peer review. Empirical benchmarks comparing the computational efficiency and accuracy of the proposed method against existing sampling-based approximations on real-world datasets are not described in the abstract, leaving practical performance gains unquantified. The scope is explicitly limited to categorical inputs; extension to continuous or mixed-type features remains an open question.
What different sources said
- arXiv cs.LGCenter
Exact Functional ANOVA Decomposition for Categorical Inputs Models
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