# A Quantum Algorithm for Shapley Value Estimation

arXiv: https://arxiv.org/abs/2301.04727 · HTML: https://mlsanity.com/paper/2301.04727/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2023.

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

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [A Shapley Value Estimation Speedup for Efficient Explainable Quantum AI](https://mlsanity.com/paper/2412.14639/) (2024)
- [QuXAI: Explainers for Hybrid Quantum Machine Learning Models](https://mlsanity.com/paper/2505.10167/) (2025)
- [Resting-state fMRI Analysis using Quantum Time-series Transformer](https://mlsanity.com/paper/2509.00711/) (2025)

## Abstract (arXiv)

In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post hoc explanations of machine learning models. However, this approach does not easily translate to eXplainable Quantum ML (XQML). Finding Shapley values can be highly computationally complex. We propose quantum algorithms which can extract Shapley values within some confidence interval. Our results perform in polynomial time. We demonstrate the validity of each approach under specific examples of cooperative voting games.