An Efficient Shapley Value Computation for the Naive Bayes Classifier
Vincent Lemaire Fabrice Clérot Marc Boullé
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.