Group Shapley with Robust Significance Testing and Its Application to Bond Recovery Rate Prediction

TL;DR

This paper introduces Group Shapley, a method for evaluating feature group importance with significance testing, applied to bond recovery rate prediction, demonstrating improved robustness and interpretability over traditional approaches.

Contribution

The paper develops a novel Group Shapley metric with a significance test based on a three-cumulant chi-square approximation, extending importance evaluation to feature groups and demonstrating its effectiveness in financial data analysis.

Findings

Group Shapley effectively identifies influential feature groups.

The significance test maintains robustness across diverse data conditions.

Application reveals market-related variables as most influential in bond recovery.

Abstract

We propose Group Shapley, a metric that extends the classical individual-level Shapley value framework to evaluate the importance of feature groups, addressing the structured nature of predictors commonly found in business and economic data. More importantly, we develop a significance testing procedure based on a three-cumulant chi-square approximation and establish the asymptotic properties of the test statistics for Group Shapley values. Our approach can effectively handle challenging scenarios, including sparse or skewed distributions and small sample sizes, outperforming alternative tests such as the Wald test. Simulations confirm that the proposed test maintains robust empirical size and demonstrates enhanced power under diverse conditions. To illustrate the method's practical relevance in advancing Explainable AI, we apply our framework to bond recovery rate predictions using a global dataset (1996-2023) comprising 2,094 observations and 98 features, grouped into 16 subgroups and five broader categories: bond characteristics, firm fundamentals, industry-specific factors, market-related variables, and macroeconomic indicators. Our results identify the market-related variables group as the most influential. Furthermore, Lorenz curves and Gini indices reveal that Group Shapley assigns feature importance more equitably compared to individual Shapley values.