类别输入模型的精确函数ANOVA分解
Exact Functional ANOVA Decomposition for Categorical Inputs Models
AI总结：
针对类别输入模型，提出一种无需假设的闭式函数ANOVA分解方法，高效处理任意依赖结构，并自然推广SHAP值。
摘要：
函数ANOVA通过将模型预测分解为主效应和高阶交互，为可解释性提供了原则性框架。对于独立特征，该分解定义明确，与SHAP值紧密相关，并作为加性可解释性的基石。然而，对于一般依赖分布，缺乏显式闭式表达式迫使实践者依赖昂贵的基于采样的近似。我们完全解决了类别输入的这一限制。通过将函数分析与离散傅里叶分析的扩展相结合，我们在没有任何假设的情况下推导出闭式分解。我们的公式计算效率非常高。它无缝地恢复了经典独立情况，并扩展到任意依赖结构，包括具有非矩形支撑的分布。此外，利用SHAP与ANOVA在独立性下的内在联系，我们的框架为一般类别设置提供了SHAP值的自然推广。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
