# Stabilizing Estimates of Shapley Values with Control Variates

arXiv: https://arxiv.org/abs/2310.07672 · HTML: https://mlsanity.com/paper/2310.07672/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [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)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [L-Shapley and C-Shapley: Efficient Model Interpretation for Structured Data](https://mlsanity.com/paper/1808.02610/) (2018)
- [Principles and Practice of Explainable Machine Learning](https://mlsanity.com/paper/2009.11698/) (2020)
- [Neuron Shapley: Discovering the Responsible Neurons](https://mlsanity.com/paper/2002.09815/) (2020)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [S-LIME: Stabilized-LIME for Model Explanation](https://mlsanity.com/paper/2106.07875/) (2021)
- [Issues with post-hoc counterfactual explanations: a discussion](https://mlsanity.com/paper/1906.04774/) (2019)
- [Sparse Projection Oblique Randomer Forests](https://mlsanity.com/paper/1506.03410/) (2015)
- [Understanding Global Feature Contributions With Additive Importance Measures](https://mlsanity.com/paper/2004.00668/) (2020)
- [Approximation Trees: Statistical Stability in Model Distillation](https://mlsanity.com/paper/1808.07573/) (2018)
- [Crime Prediction Using Machine Learning and Deep Learning: A Systematic Review and Future Directions](https://mlsanity.com/paper/2303.16310/) (2023)
- [Exact Shapley Values for Local and Model-True Explanations of Decision Tree Ensembles](https://mlsanity.com/paper/2112.10592/) (2021)

## Built on by (most cited first, 9 of 9)

- [Statistical Significance of Feature Importance Rankings](https://mlsanity.com/paper/2401.15800/) (2024)
- [Improving the Weighting Strategy in KernelSHAP](https://mlsanity.com/paper/2410.04883/) (2024)
- [shapr: Explaining Machine Learning Models with Conditional Shapley Values in R and Python](https://mlsanity.com/paper/2504.01842/) (2025)
- [On the Fragility of Contribution Score Computation in Federated Learning](https://mlsanity.com/paper/2509.19921/) (2025)
- [Challenges in Enabling Private Data Valuation](https://mlsanity.com/paper/2603.00342/) (2026)
- [Antithetic Sampling for Top-k Shapley Identification](https://mlsanity.com/paper/2504.02019/) (2025)
- [Beyond performance-wise Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2602.22470/) (2026)
- [Rethinking XAI Evaluation: A Human-Centered Audit of Shapley Benchmarks in High-Stakes Settings](https://mlsanity.com/paper/2604.22662/) (2026)
- [Measuring Explainer Stability via Attribution Separability](https://mlsanity.com/paper/2608.02697/) (2026)

## Abstract (arXiv)

Shapley values are among the most popular tools for explaining predictions of blackbox machine learning models. However, their high computational cost motivates the use of sampling approximations, inducing a considerable degree of uncertainty. To stabilize these model explanations, we propose ControlSHAP, an approach based on the Monte Carlo technique of control variates. Our methodology is applicable to any machine learning model and requires virtually no extra computation or modeling effort. On several high-dimensional datasets, we find it can produce dramatic reductions in the Monte Carlo variability of Shapley estimates.