An Efficient Shapley Value Computation for the Naive Bayes Classifier

TL;DR

This paper introduces an exact analytical method for computing Shapley values in naive Bayes classifiers, enabling efficient and interpretable feature importance analysis suitable for large datasets.

Contribution

It provides the first analytical formula for Shapley values in naive Bayes classifiers, improving computational efficiency and interpretability.

Findings

The proposed Shapley method is computationally efficient for large datasets.

It yields informative feature importance insights comparable to existing methods.

Empirical results show low complexity and high interpretability.

Abstract

Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so many intelligibility algorithms available today. Among them, Shapley value estimation algorithms are intelligibility methods based on cooperative game theory. In the case of the naive Bayes classifier, and to our knowledge, there is no ``analytical" formulation of Shapley values. This article proposes an exact analytic expression of Shapley values in the special case of the naive Bayes Classifier. We analytically compare this Shapley proposal, to another frequently used indicator, the Weight of Evidence (WoE) and provide an empirical comparison of our proposal with (i) the WoE and (ii) KernelShap results on real world datasets, discussing similar and dissimilar results. The results show that our Shapley proposal for the naive Bayes classifier provides informative results with low algorithmic complexity so that it can be used on very large datasets with extremely low computation time.