# How to safely discard features based on aggregate SHAP values

arXiv: https://arxiv.org/abs/2503.23111 · HTML: https://mlsanity.com/paper/2503.23111/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 40 references that are in the map.
- First posted on arXiv 29 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Impossibility Theorems for Feature Attribution](https://mlsanity.com/paper/2212.11870/) (2022)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Framework for Evaluating Faithfulness of Local Explanations](https://mlsanity.com/paper/2202.00734/) (2022)
- [Global Aggregations of Local Explanations for Black Box models](https://mlsanity.com/paper/1907.03039/) (2019)
- [Rethinking Data Shapley for Data Selection Tasks: Misleads and Merits](https://mlsanity.com/paper/2405.03875/) (2024)
- [Feature Importance: A Closer Look at Shapley Values and LOCO](https://mlsanity.com/paper/2303.05981/) (2023)
- [A Guide to Feature Importance Methods for Scientific Inference](https://mlsanity.com/paper/2404.12862/) (2024)
- [A Theory of Interpretable Approximations](https://mlsanity.com/paper/2406.10529/) (2024)
- [Accelerating the Global Aggregation of Local Explanations](https://mlsanity.com/paper/2312.07991/) (2023)

## Built on by (most cited first, 1 of 1)

- [Feature Attribution from First Principles](https://mlsanity.com/paper/2505.24729/) (2025)

## Abstract (arXiv)

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.