# RKHS-SHAP: Shapley Values for Kernel Methods

arXiv: https://arxiv.org/abs/2110.09167 · HTML: https://mlsanity.com/paper/2110.09167/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 23 of 23)

- [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)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (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)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [On Locality of Local Explanation Models](https://mlsanity.com/paper/2106.14648/) (2021)
- [Kernel Dependence Regularizers and Gaussian Processes with Applications to Algorithmic Fairness](https://mlsanity.com/paper/1911.04322/) (2019)
- [Bayesian Learning of Kernel Embeddings](https://mlsanity.com/paper/1603.02160/) (2016)
- [Kernel Conditional Density Operators](https://mlsanity.com/paper/1905.11255/) (2019)
- [Cohort Shapley value for algorithmic fairness](https://mlsanity.com/paper/2105.07168/) (2021)
- [Biased Models Have Biased Explanations](https://mlsanity.com/paper/2012.10986/) (2020)
- [Kernel Adaptive Metropolis-Hastings](https://mlsanity.com/paper/1307.5302/) (2013)

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

- [Looping in the Human Collaborative and Explainable Bayesian Optimization](https://mlsanity.com/paper/2310.17273/) (2023)
- [Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models](https://mlsanity.com/paper/2305.15167/) (2023)
- [Identifying regions of importance in wall-bounded turbulence through explainable deep learning](https://mlsanity.com/paper/2302.01250/) (2023)
- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [Explaining Preferences with Shapley Values](https://mlsanity.com/paper/2205.13662/) (2022)
- [Exact Shapley Attributions in Quadratic-time for FANOVA Gaussian Processes](https://mlsanity.com/paper/2508.14499/) (2025)
- [Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals](https://mlsanity.com/paper/2505.13118/) (2025)
- [Amortized Linear-time Exact Shapley Value for Product-Kernel Methods](https://mlsanity.com/paper/2505.16516/) (2025)
- [Gated Domain Units for Multi-source Domain Generalization](https://mlsanity.com/paper/2206.12444/) (2022)
- [UbiQTree: Uncertainty Quantification in XAI with Tree Ensembles](https://mlsanity.com/paper/2508.09639/) (2025)
- [Fast Calculation of Feature Contributions in Boosting Trees](https://mlsanity.com/paper/2407.03515/) (2024)
- [Understanding Data Influence with Differential Approximation](https://mlsanity.com/paper/2508.14648/) (2025)
- [Explaining Kernel Clustering via Decision Trees](https://mlsanity.com/paper/2402.09881/) (2024)
- [Tractable Shapley Values and Interactions via Tensor Networks](https://mlsanity.com/paper/2510.22138/) (2025)
- [Energy-Based Model for Accurate Estimation of Shapley Values in Feature Attribution](https://mlsanity.com/paper/2404.01078/) (2024)
- [Unlearning-based Neural Interpretations](https://mlsanity.com/paper/2410.08069/) (2024)
- [Explanation Design in Strategic Learning: Sufficient Explanations that Induce Non-harmful Responses](https://mlsanity.com/paper/2502.04058/) (2025)
- [STRIDE: Subset-Free Functional Decomposition for XAI in Tabular Settings](https://mlsanity.com/paper/2509.09070/) (2025)
- [Returning The Favour: When Regression Benefits From Probabilistic Causal Knowledge](https://mlsanity.com/paper/2301.11214/) (2023)
- [A novel application of Shapley values for large multidimensional time-series data: Applying explainable AI to a DNA profile classification neural network](https://mlsanity.com/paper/2409.18156/) (2024)
- [Interpretable Load Forecasting via Representation Learning of Geo-distributed Meteorological Factors](https://mlsanity.com/paper/2501.02241/) (2025)
- [Kernel Quantile Embeddings and Associated Probability Metrics](https://mlsanity.com/paper/2505.20433/) (2025)
- [An Enhanced Focal Loss Function to Mitigate Class Imbalance in Auto Insurance Fraud Detection with Explainable AI](https://mlsanity.com/paper/2508.02283/) (2025)
- [SHAP-Guided Kernel Actor-Critic for Explainable Reinforcement Learning](https://mlsanity.com/paper/2512.05291/) (2025)
- [GRALIS: Fusing Coalition and Gradient Attribution with Closed-Form Conservation Error and Finite-Sample Guarantees](https://mlsanity.com/paper/2605.05480/) (2026)
- [ConfoundingSHAP: Quantifying confounding strength in causal inference](https://mlsanity.com/paper/2605.10533/) (2026)
- [Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks](https://mlsanity.com/paper/2605.24084/) (2026)
- [ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation](https://mlsanity.com/paper/2606.02247/) (2026)
- [Dataset Distillation by Influence Matching](https://mlsanity.com/paper/2607.16859/) (2026)

## Abstract (arXiv)

Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to different machine learning model interpretation tasks, such as linear models, tree ensembles and deep networks. By analysing SVs from a functional perspective, we propose textscRKHS-SHAP, an attribution method for kernel machines that can efficiently compute both Interventional and Observational Shapley values using kernel mean embeddings of distributions. We show theoretically that our method is robust with respect to local perturbations - a key yet often overlooked desideratum for consistent model interpretation. Further, we propose Shapley regulariser, applicable to a general empirical risk minimisation framework, allowing learning while controlling the level of specific feature's contributions to the model. We demonstrate that the Shapley regulariser enables learning which is robust to covariate shift of a given feature and fair learning which controls the SVs of sensitive features.