Building a Bridge Between the Shapley Value, Prime Implicants and Counterfactual Explanations: a Theoretical Analysis

Hénoïk Willot
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:7387-7402, 2026.

Abstract

Since the introduction of SHAP, many methods adapted the idea of using the {Shapley} value formula as a way to measure the importance of a feature in the decision of a model. However, computing this value theoretically imply to relearn the model with and without the feature for all subsets of features. To avoid this, the methods rely on sampling to compute an expectation to measure a mean impact of a feature. In this paper we investigate theoretically if we could, and under which conditions, build and use a textbook cooperative game with the help of other explanation techniques, Prime Implicants and Counterfactual explanations, for computing {Shapley} values for interpretability. We propose detailed and iterative analysis of the number of remaining explanations during the enumeration of the explanations, alongside the computation of the {Shapley} value and its upper and lower bounds.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-willot26a, title = {Building a Bridge Between the {Shapley} Value, Prime Implicants and Counterfactual Explanations: a Theoretical Analysis}, author = {Willot, H\'{e}no\"{i}k}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {7387--7402}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/willot26a/willot26a.pdf}, url = {https://proceedings.mlr.press/v337/willot26a.html}, abstract = {Since the introduction of SHAP, many methods adapted the idea of using the {Shapley} value formula as a way to measure the importance of a feature in the decision of a model. However, computing this value theoretically imply to relearn the model with and without the feature for all subsets of features. To avoid this, the methods rely on sampling to compute an expectation to measure a mean impact of a feature. In this paper we investigate theoretically if we could, and under which conditions, build and use a textbook cooperative game with the help of other explanation techniques, Prime Implicants and Counterfactual explanations, for computing {Shapley} values for interpretability. We propose detailed and iterative analysis of the number of remaining explanations during the enumeration of the explanations, alongside the computation of the {Shapley} value and its upper and lower bounds.} }
Endnote
%0 Conference Paper %T Building a Bridge Between the Shapley Value, Prime Implicants and Counterfactual Explanations: a Theoretical Analysis %A Hénoïk Willot %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-willot26a %I PMLR %P 7387--7402 %U https://proceedings.mlr.press/v337/willot26a.html %V 337 %X Since the introduction of SHAP, many methods adapted the idea of using the {Shapley} value formula as a way to measure the importance of a feature in the decision of a model. However, computing this value theoretically imply to relearn the model with and without the feature for all subsets of features. To avoid this, the methods rely on sampling to compute an expectation to measure a mean impact of a feature. In this paper we investigate theoretically if we could, and under which conditions, build and use a textbook cooperative game with the help of other explanation techniques, Prime Implicants and Counterfactual explanations, for computing {Shapley} values for interpretability. We propose detailed and iterative analysis of the number of remaining explanations during the enumeration of the explanations, alongside the computation of the {Shapley} value and its upper and lower bounds.
APA
Willot, H.. (2026). Building a Bridge Between the Shapley Value, Prime Implicants and Counterfactual Explanations: a Theoretical Analysis. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:7387-7402 Available from https://proceedings.mlr.press/v337/willot26a.html.

Related Material