$\phi$-Table: A Statistical Explanation for Global SHAP

TL;DR

The paper introduces the $$-table, a SHAP-based statistical tool that provides detailed global explanations for black-box regression models, including feature effects, uncertainty, and stability.

Contribution

It extends SHAP feature importance rankings into a comprehensive statistical explanation by integrating linear surrogate models and uncertainty measures.

Findings

The $$-table effectively reveals feature directions and uncertainties.

It demonstrates high surrogate fidelity and coefficient stability across various datasets.

The method enhances interpretability of black-box models beyond simple rankings.

Abstract

Global SHAP explanations are typically presented as feature-importance rankings, which identify variables that matter to a black-box model but do not indicate whether their effects admit clear directional summaries, how uncertain those summaries are, or how faithfully they represent the fitted response. This paper proposes the $\phi$-table, a SHAP-based statistical explanation table for tabular black-box regression models. The procedure selects features by SHAP importance and fits a standardized linear surrogate to the fitted model response $f(X)$, reporting SHAP importance together with model-response coefficients, uncertainty summaries, surrogate fidelity, and bootstrap coefficient stability. The resulting coefficients are interpreted as projections of the fitted model response onto the SHAP-selected feature set. Across synthetic, semi-synthetic, and real-data experiments, the $\phi$-table extends ranking-only SHAP into a statistical global explanation by exposing direction, uncertainty, fidelity, and stability as distinct components of fitted model behavior.