# Shapley Values with Uncertain Value Functions

arXiv: https://arxiv.org/abs/2301.08086 · HTML: https://mlsanity.com/paper/2301.08086/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 7 of 7)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [Principles and Practice of Explainable Machine Learning](https://mlsanity.com/paper/2009.11698/) (2020)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)

## Built on by (most cited first, 1 of 1)

- [Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning](https://mlsanity.com/paper/2301.09138/) (2023)

## Abstract (arXiv)

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random effects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational effort.