We propose a novel method for measuring the importance and usefulness of predictor variables (features) in supervised machine learning, which makes use of concepts from cooperative game theory. The basic idea of our approach is to consider subsets of variables as coalitions, and their predictive performance as a payo . This approach acknowledges the fact that the usefulness of a feature in a learning context strongly depends, not only on the learning method being used, but also on the other features being available.
A theoretically appealing measure of the importance of an individual feature
is the Shapley value [
As another aspect speci c to machine learning, let us note that the Shapley values of each feature can change with varying sample size, due to e ects such as over tting. Motivated by this observation, we introduce the concept of a Shapley curve, which depicts the (weighted average) contribution of a feature to the learning curve (expected performance as a function of the sample size).
We develop an approximation technique for estimating Shapley values, which
is e cient in the number of models that need to be trained and validated.
Moreover, to estimate Shapley curves, we propose a hierarchical Bayes approach
that does not require an evaluation of all possible subsets of features on di erent
sample sizes. Last but not least, leveraging related techniques for extrapolating
learning curves [