How to safely discard features based on aggregate SHAP values

2025-03-29

AI Summary

This work exposes a security vulnerability in feature selection based on aggregated SHAP values: averaging absolute SHAP values over the original data support set may erroneously eliminate important features, as SHAP computation requires extrapolation beyond the support—where dependencies on specific features can be deliberately concealed via adversarial function construction. To address this, we propose a novel aggregation paradigm over an expanded support set—the Cartesian product of marginal feature distributions—and provide the first rigorous proof that small aggregated SHAP or KernelSHAP values on this domain guarantee safe feature removal. We introduce the Shapley Lie algebra to offer a new theoretical lens, and show that column-wise random permutations provably ensure safety in standard SHAP practice. This work establishes the first theoretical guarantees for KernelSHAP, delivers a verifiable criterion for feature deletion, and empirically validates its effectiveness in identifying redundant features, simplifying models, and enhancing interpretability.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Natural Language Processing: Safety and Robustness
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

SHAP is one of the most popular local feature-attribution methods. Given a function f and an input x, it quantifies each feature's contribution to f(x). Recently, SHAP has been increasingly used for global insights: practitioners average the absolute SHAP values over many data points to compute global feature importance scores, which are then used to discard unimportant features. In this work, we investigate the soundness of this practice by asking whether small aggregate SHAP values necessarily imply that the corresponding feature does not affect the function. Unfortunately, the answer is no: even if the i-th SHAP value is 0 on the entire data support, there exist functions that clearly depend on Feature i. The issue is that computing SHAP values involves evaluating f on points outside of the data support, where f can be strategically designed to mask its dependence on Feature i. To address this, we propose to aggregate SHAP values over the extended support, which is the product of the marginals of the underlying distribution. With this modification, we show that a small aggregate SHAP value implies that we can safely discard the corresponding feature. We then extend our results to KernelSHAP, the most popular method to approximate SHAP values in practice. We show that if KernelSHAP is computed over the extended distribution, a small aggregate value justifies feature removal. This result holds independently of whether KernelSHAP accurately approximates true SHAP values, making it one of the first theoretical results to characterize the KernelSHAP algorithm itself. Our findings have both theoretical and practical implications. We introduce the Shapley Lie algebra, which offers algebraic insights that may enable a deeper investigation of SHAP and we show that randomly permuting each column of the data matrix enables safely discarding features based on aggregate SHAP and KernelSHAP values.

Problem

• Investigates soundness of discarding features using aggregate SHAP values
• Proposes aggregating SHAP values over extended support for safe feature removal
• Extends results to KernelSHAP, justifying feature removal under modified conditions

Innovation

• Aggregate SHAP values over extended support
• Extend results to KernelSHAP algorithm
• Introduce Shapley Lie algebra insights