A Multilinear Sampling Algorithm to Estimate Shapley Values

TL;DR

This paper introduces a multilinear extension-based sampling algorithm for more efficient and accurate estimation of Shapley values in machine learning models, especially for complex models and larger feature sets.

Contribution

It presents a novel multilinear sampling method that improves the efficiency and accuracy of Shapley value estimation in machine learning applications.

Findings

Reduces variance in Shapley value estimates

Applicable to multi-class classification and regression

Demonstrates improved accuracy on datasets with MLPs

Abstract

Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data science and machine learning. However, the time complexity to compute Shapley values based on the original formula is exponential, and as the number of features increases, this becomes infeasible. Castro et al. [1] developed a sampling algorithm, to estimate Shapley values. In this work, we propose a new sampling method based on a multilinear extension technique as applied in game theory. The aim is to provide a more efficient (sampling) method for estimating Shapley values. Our method is applicable to any machine learning model, in particular for either multi-class classifications or regression problems. We apply the method to estimate Shapley values for multilayer perceptrons (MLPs) and through experimentation on two datasets, we demonstrate that our method provides more accurate estimations of the Shapley values by reducing the variance of the sampling statistics.