# Stability theory of game-theoretic group feature explanations for machine learning models

arXiv: https://arxiv.org/abs/2102.10878 · HTML: https://mlsanity.com/paper/2102.10878/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2021.

## Built on by (most cited first, 4 of 4)

- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Model-agnostic bias mitigation methods with regressor distribution control for Wasserstein-based fairness metrics](https://mlsanity.com/paper/2111.11259/) (2021)
- [Approximation of group explainers with coalition structure using Monte Carlo sampling on the product space of coalitions and features](https://mlsanity.com/paper/2303.10216/) (2023)
- [Explainable post-training bias mitigation with distribution-based fairness metrics](https://mlsanity.com/paper/2504.01223/) (2025)

## Abstract (arXiv)

In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the conditional and marginal expectations. The first part of our work formulates a stability theory for these explanation operators by establishing certain bounds for both marginal and conditional explanations. The differences between the two games are then elucidated, such as showing that the marginal explanations can become discontinuous on some naturally-designed domains, while the conditional explanations remain stable. In the second part of our work, group explanation methodologies are devised based on game values with coalition structure, where the features are grouped based on dependencies. We show analytically that grouping features this way has a stabilizing effect on the marginal operator on both group and individual levels, and allows for the unification of marginal and conditional explanations. Our results are verified in a number of numerical experiments where an information-theoretic measure of dependence is used for grouping.