# Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression

arXiv: https://arxiv.org/abs/2012.01536 · HTML: https://mlsanity.com/paper/2012.01536/

## Key facts

- Cited by 154 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2020.

## Built on by (most cited first, 30 of 154)

- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [Rethinking Explainability as a Dialogue: A Practitioner's Perspective](https://mlsanity.com/paper/2202.01875/) (2022)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments](https://mlsanity.com/paper/2206.10013/) (2022)
- [Learning to Estimate Shapley Values with Vision Transformers](https://mlsanity.com/paper/2206.05282/) (2022)
- [Everybody Prune Now: Structured Pruning of LLMs with only Forward Passes](https://mlsanity.com/paper/2402.05406/) (2024)
- [shapiq: Shapley Interactions for Machine Learning](https://mlsanity.com/paper/2410.01649/) (2024)
- [Explaining a Series of Models by Propagating Shapley Values](https://mlsanity.com/paper/2105.00108/) (2021)
- [Explain Any Concept: Segment Anything Meets Concept-Based Explanation](https://mlsanity.com/paper/2305.10289/) (2023)
- [Defining and Quantifying the Emergence of Sparse Concepts in DNNs](https://mlsanity.com/paper/2111.06206/) (2021)
- [WeightedSHAP: analyzing and improving Shapley based feature attributions](https://mlsanity.com/paper/2209.13429/) (2022)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [Approximating the Shapley Value without Marginal Contributions](https://mlsanity.com/paper/2302.00736/) (2023)
- [On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results](https://mlsanity.com/paper/2104.08015/) (2021)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [RKHS-SHAP: Shapley Values for Kernel Methods](https://mlsanity.com/paper/2110.09167/) (2021)
- [On Locality of Local Explanation Models](https://mlsanity.com/paper/2106.14648/) (2021)
- [The Shapley Value of Classifiers in Ensemble Games](https://mlsanity.com/paper/2101.02153/) (2021)
- [Provably Accurate Shapley Value Estimation via Leverage Score Sampling](https://mlsanity.com/paper/2410.01917/) (2024)
- [SHAFF: Fast and consistent SHApley eFfect estimates via random Forests](https://mlsanity.com/paper/2105.11724/) (2021)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [groupShapley: Efficient prediction explanation with Shapley values for feature groups](https://mlsanity.com/paper/2106.12228/) (2021)
- [Stochastic Amortization: A Unified Approach to Accelerate Feature and Data Attribution](https://mlsanity.com/paper/2401.15866/) (2024)
- [CoRTX: Contrastive Framework for Real-time Explanation](https://mlsanity.com/paper/2303.02794/) (2023)
- [Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models](https://mlsanity.com/paper/2305.15167/) (2023)

## Abstract (arXiv)

The Shapley value concept from cooperative game theory has become a popular technique for interpreting ML models, but efficiently estimating these values remains challenging, particularly in the model-agnostic setting. Here, we revisit the idea of estimating Shapley values via linear regression to understand and improve upon this approach. By analyzing the original KernelSHAP alongside a newly proposed unbiased version, we develop techniques to detect its convergence and calculate uncertainty estimates. We also find that the original version incurs a negligible increase in bias in exchange for significantly lower variance, and we propose a variance reduction technique that further accelerates the convergence of both estimators. Finally, we develop a version of KernelSHAP for stochastic cooperative games that yields fast new estimators for two global explanation methods.