aiqbench analysis
This research resolves a key computational bottleneck in model interpretability by deriving a closed-form Exact Functional ANOVA decomposition for categorical inputs with arbitrary dependence structures. By eliminating the need for costly sampling-based approximations, the method offers a highly efficient generalization of SHAP values that seamlessly handles non-rectangular support distributions. This advancement provides a robust theoretical foundation for additive explainability in complex, dependent feature settings without relying on independence assumptions.
Exact Functional ANOVA Decomposition for Categorical Inputs Models
arXiv:2603.02673v2 Announce Type: replace-cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2603.02673 [stat.ML]
(or arXiv:2603.02673v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2603.02673 Focus to learn more arXiv-issued DOI via DataCite
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