# Approximation of group explainers with coalition structure using Monte Carlo sampling on the product space of coalitions and features

arXiv: https://arxiv.org/abs/2303.10216 · HTML: https://mlsanity.com/paper/2303.10216/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 53 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 19 of 19)

- [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)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Shapley Flow: A Graph-based Approach to Interpreting Model Predictions](https://mlsanity.com/paper/2010.14592/) (2020)
- [Explainable Neural Networks based on Additive Index Models](https://mlsanity.com/paper/1806.01933/) (2018)
- [Locally Interpretable Models and Effects based on Supervised Partitioning (LIME-SUP)](https://mlsanity.com/paper/1806.00663/) (2018)
- [Using Shapley Values and Variational Autoencoders to Explain Predictive Models with Dependent Mixed Features](https://mlsanity.com/paper/2111.13507/) (2021)
- [Self-explaining AI as an alternative to interpretable AI](https://mlsanity.com/paper/2002.05149/) (2020)
- [Explaining predictive models using Shapley values and non-parametric vine copulas](https://mlsanity.com/paper/2102.06416/) (2021)
- [Measuring dependence powerfully and equitably](https://mlsanity.com/paper/1505.02213/) (2015)
- [Stability theory of game-theoretic group feature explanations for machine learning models](https://mlsanity.com/paper/2102.10878/) (2021)
- [On marginal feature attributions of tree-based models](https://mlsanity.com/paper/2302.08434/) (2023)
- [Post-Radiotherapy PET Image Outcome Prediction by Deep Learning under Biological Model Guidance: A Feasibility Study of Oropharyngeal Cancer Application](https://mlsanity.com/paper/2105.10650/) (2021)
- [An Empirical Study of Leading Measures of Dependence](https://mlsanity.com/paper/1505.02214/) (2015)

## Built on by (most cited first, 2 of 2)

- [MBExplainer: Multilevel bandit-based explanations for downstream models with augmented graph embeddings](https://mlsanity.com/paper/2411.00287/) (2024)
- [Explainable post-training bias mitigation with distribution-based fairness metrics](https://mlsanity.com/paper/2504.01223/) (2025)

## Abstract (arXiv)

In recent years, many Machine Learning (ML) explanation techniques have been designed using ideas from cooperative game theory. These game-theoretic explainers suffer from high complexity, hindering their exact computation in practical settings. In our work, we focus on a wide class of linear game values, as well as coalitional values, for the marginal game based on a given ML model and predictor vector. By viewing these explainers as expectations over appropriate sample spaces, we design a novel Monte Carlo sampling algorithm that estimates them at a reduced complexity that depends linearly on the size of the background dataset. We set up a rigorous framework for the statistical analysis and obtain error bounds for our sampling methods. The advantage of this approach is that it is fast, easily implementable, and model-agnostic. Furthermore, it has similar statistical accuracy as other known estimation techniques that are more complex and model-specific. We provide rigorous proofs of statistical convergence, as well as numerical experiments whose results agree with our theoretical findings.