发表机构
University of Naples “Federico II”; Department of Economics and Statistics, University of Naples “Federico II”（那不勒斯费德里科二世大学; 那不勒斯费德里科二世大学经济统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种条件Shapley特征重要性的半参数推断方法，通过单步估计器与U统计量校正消除偏差，实现渐近正态推断，并在模拟和真实数据中验证其有效性。
AI 中文摘要
Shapley值广泛用于事后特征归因，但大多数估计器返回点数量且不量化不确定性，流行的实现从边际分布中采样联盟外特征，当特征相关时会错误归因重要性。本文研究条件公式，其中联盟外特征在其真实条件分布下被积分掉。目标是全局的、基于损失的重要性，将条件值函数与SAGE式损失聚合配对。我们提出一种单步估计器，采用K折交叉拟合和平方损失的U统计量校正，以消除朴素插入法的蒙特卡洛偏差；在双稳健率条件下，它是$\sqrt{n}$一致的且渐近正态，所得的Wald区间达到名义覆盖率。Pinsker型界量化了错误指定工作copula类的偏差，而vine copula保持条件采样的可处理性。在n=500的高斯设计研究中，95%区间的经验覆盖率在所有特征中介于0.91和0.96之间，检验在0.05处保持其I型错误率，并对中等信号达到功效1。应用于UCI Concrete和California Housing数据，该方法以Bonferroni控制的显著性识别条件信息特征。
英文摘要
Shapley values are widely used for post-hoc feature attribution, but most estimators return point quantities and do not quantify uncertainty, and popular implementations sample out-of-coalition features from their marginal distribution, which misattributes importance when features are dependent. This paper studies the conditional formulation, in which out-of-coalition features are integrated out under their true conditional distribution. The target is a global, loss-based importance that pairs a conditional value function with a SAGE-style loss aggregation. We propose a one-step estimator with K-fold cross-fitting and a U-statistic correction of the squared loss that removes the Monte Carlo bias of the naive plug-in; it is $\sqrt{n}$-consistent and asymptotically normal under double-robust rate conditions, and the resulting Wald interval attains nominal coverage. A Pinsker-type bound quantifies the bias from misspecifying the working copula class, while vine copulas keep conditional sampling tractable. In a Gaussian design study with n= 500, the empirical coverage of the 95% interval lies between 0.91 and 0.96 across all features, the test holds its Type-I rate at 0.05, and it reaches power one for moderate signals. Applied to the UCI Concrete and California Housing data, the method identifies the conditionally informative features with Bonferroni-controlled significance.
