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

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