How to safely discard features based on aggregate SHAP values

Robi Bhattacharjee, Karolin Frohnapfel, Ulrike von Luxburg
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:280-314, 2025.

Abstract

SHAP is one of the most popular \textit{local} feature-attribution methods. Given a function $f$ and an input $x \in \mathbb{R}^d$, it quantifies each feature’s contribution to $f(x)$. Recently, SHAP has been increasingly used for \textit{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 equals $0$ 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 \textit{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 KernelSHAP 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 a simple preprocessing step – randomly permuting each column of the data matrix – enables safely discarding features based on aggregate SHAP and KernelSHAP values.

Cite this Paper

BibTeX
@InProceedings{pmlr-v291-bhattacharjee25a, title = {How to safely discard features based on aggregate SHAP values}, author = {Bhattacharjee, Robi and Frohnapfel, Karolin and von Luxburg, Ulrike}, booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory}, pages = {280--314}, year = {2025}, editor = {Haghtalab, Nika and Moitra, Ankur}, volume = {291}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--04 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v291/main/assets/bhattacharjee25a/bhattacharjee25a.pdf}, url = {https://proceedings.mlr.press/v291/bhattacharjee25a.html}, abstract = {SHAP is one of the most popular \textit{local} feature-attribution methods. Given a function $f$ and an input $x \in \mathbb{R}^d$, it quantifies each feature’s contribution to $f(x)$. Recently, SHAP has been increasingly used for \textit{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 equals $0$ 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 \textit{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 KernelSHAP 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 a simple preprocessing step – randomly permuting each column of the data matrix – enables safely discarding features based on aggregate SHAP and KernelSHAP values.} }
Endnote
%0 Conference Paper %T How to safely discard features based on aggregate SHAP values %A Robi Bhattacharjee %A Karolin Frohnapfel %A Ulrike von Luxburg %B Proceedings of Thirty Eighth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2025 %E Nika Haghtalab %E Ankur Moitra %F pmlr-v291-bhattacharjee25a %I PMLR %P 280--314 %U https://proceedings.mlr.press/v291/bhattacharjee25a.html %V 291 %X SHAP is one of the most popular \textit{local} feature-attribution methods. Given a function $f$ and an input $x \in \mathbb{R}^d$, it quantifies each feature’s contribution to $f(x)$. Recently, SHAP has been increasingly used for \textit{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 equals $0$ 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 \textit{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 KernelSHAP 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 a simple preprocessing step – randomly permuting each column of the data matrix – enables safely discarding features based on aggregate SHAP and KernelSHAP values.
APA
Bhattacharjee, R., Frohnapfel, K. & von Luxburg, U.. (2025). How to safely discard features based on aggregate SHAP values. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:280-314 Available from https://proceedings.mlr.press/v291/bhattacharjee25a.html.

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