# Shapley Values: Paired-Sampling Approximations

arXiv: https://arxiv.org/abs/2508.12947 · HTML: https://mlsanity.com/paper/2508.12947/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [Bounding the Estimation Error of Sampling-based Shapley Value Approximation](https://mlsanity.com/paper/1306.4265/) (2013)

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

- [PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression](https://mlsanity.com/paper/2601.18608/) (2026)
- [An Odd Estimator for Shapley Values](https://mlsanity.com/paper/2602.01399/) (2026)

## Abstract (arXiv)

Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes to an output (prediction). These credits are then used to explain the prediction. The only limitation in computing the Shapley values (credits) for many different predictions is of computational nature. There are two popular sampling approximations, sampling KernelSHAP and sampling PermutationSHAP. Our first novel contributions are asymptotic normality results for these sampling approximations. Next, we show that the paired-sampling approaches provide exact results in case of interactions being of maximal order two. Furthermore, the paired-sampling PermutationSHAP possesses the additive recovery property, whereas its kernel counterpart does not.