Approximate Shapley value estimation using sampling without replacement and variance estimation via the new Symmetric bootstrap and the Doubled half bootstrap

TL;DR

This paper enhances the KernelSHAP algorithm by integrating sampling without replacement using Wallenius' distribution and introduces new bootstrap methods for variance estimation, demonstrating improved or comparable performance in simulations.

Contribution

It proposes a novel sampling method for KernelSHAP using Wallenius' distribution and introduces the Symmetric and Doubled half bootstrap techniques for variance estimation.

Findings

Bootstrap methods perform better or equally well in simulations.

The new KernelSHAP performs similarly to existing methods in practice.

Sampling without replacement improves estimation stability.

Abstract

In this paper I consider improving the KernelSHAP algorithm. I suggest to use the Wallenius' noncentral hypergeometric distribution for sampling the number of coalitions and perform sampling without replacement, so that the KernelSHAP estimation framework is improved further. I also introduce the Symmetric bootstrap to calculate the standard deviations and also use the Doubled half bootstrap method to compare the performance. The new bootstrap algorithm performs better or equally well in the two simulation studies performed in this paper. The new KernelSHAP algorithm performs similarly as the improved KernelSHAP method in the state-of-the-art R-package shapr, which samples coalitions with replacement in one of the options