提出闭式解的广义函数ANOVA，统一解释模型主效应与交互作用。
Generalized Functional ANOVA in Closed-Form: A Unified View of Additive Explanations
- 基于希尔伯特空间构建显式正交基，实现连续输入下的可计算分解。
- 在真实依赖输入场景中，首次获得闭式表达的函数分解形式。
- 模型无关算法高效估计分解，优于当前主流解释方法。
函数ANOVA（即霍夫丁分解）通过将模型预测分解为主效应和高阶交互项，为可解释性提供了严谨框架。对于独立输入，该经典分解具有显式形式，与SHAP值、广义加性模型及正交多项式展开密切相关，是加性解释的核心工具。然而，在更普遍且现实的依赖输入场景中，获得可处理的表示并从数据中估计分解仍具挑战。本文针对连续输入，结合希尔伯特空间方法与广义函数ANOVA，构建了显式的瑞斯基底（Riesz Basis），使分解可直接计算。该公式恢复了独立情形下的经典正交分解，并在此基础上提出一种简单而强大的模型无关算法，可从样本数据估计分解。实验对比表明，该方法在多种场景下均显著优于现有先进解释方法。
原文摘要 · Abstract (English)
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition is explicit. It is closely connected to SHAP values, generalized additive models, and orthogonal polynomial expansions, and therefore constitutes a fundamental tool for additive explainability. In the more general and realistic dependent setting, however, obtaining a tractable representation and estimating the decomposition from data remain challenging. In this work, we address this problem for continuous inputs. By combining Hilbert space methods with the generalized functional ANOVA, we build an explicit decomposition Riesz Basis allowing to easily compute the decomposition. Our formulation recovers the classical independent case and its associated orthogonal decomposition. Building on this representation, we propose a simple but mighty algorithm to estimate the decomposition from a data sample in a model-agnostic setting and we compare it empirically with several state-of-the-art explanation methods, demonstrating the power of the approach.
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