Semiparametric Inference for Conditional Shapley Feature Importance

• URL: http://arxiv.org/abs/2609.10313v2
• Date: Mon, 14 Sep 2026 07:29:41 GMT
• Title: Semiparametric Inference for Conditional Shapley Feature Importance
• Abstract summary: This paper studies the conditional formulation, in which out-of-coalition features are integrated out under their true conditional distribution.<n>We propose a one-step estimator with K-fold cross-fitting and a U-statistic correction of the squared loss interval.<n>A Pinsker-type bound quantifies the bias from misspecifying the working copula class, while vine copulas keep conditional sampling tractable.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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