RKHS-SHAP: Shapley Values for Kernel Methods

TL;DR

RKHS-SHAP introduces an efficient kernel-based method for computing Shapley values for feature attribution in kernel machines, offering robustness and fairness in model interpretation.

Contribution

The paper develops RKHS-SHAP, a novel approach for calculating Shapley values in kernel methods, and introduces a Shapley regulariser for robust and fair learning.

Findings

Efficient computation of interventional and observational Shapley values using kernel mean embeddings.

Theoretical robustness of the method to local perturbations.

Shapley regulariser improves robustness to covariate shift and fairness in models.

Abstract

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 \textsc{RKHS-SHAP}, an attribution method for kernel machines that can efficiently compute both \emph{Interventional} and \emph{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 \emph{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.