Title: Feature importance scores and lossless feature pruning using Banzhaf power indices,
Abstract: Understanding the influence of features in machine learning is crucial to
interpreting models and selecting the best features for classification. In this
work we propose the use of principles from coalitional game theory to reason
about importance of features. In particular, we propose the use of the Banzhaf
power index as a measure of influence of features on the outcome of a
classifier. We show that features having Banzhaf power index of zero can be
losslessly pruned without damage to classifier accuracy. Computing the power
indices does not require having access to data samples. However, if samples are
available, the indices can be empirically estimated. We compute Banzhaf power
indices for a neural network classifier on real-life data, and compare the
results with gradient-based feature saliency, and coefficients of a logistic
regression model with $L_1$ regularization.