  This paper introduces and develops a novel variable importance score function
in the context of ensemble learning and demonstrates its appeal both
theoretically and empirically. Our proposed score function is simple and more
straightforward than its counterpart proposed in the context of random forest,
and by avoiding permutations, it is by design computationally more efficient
than the random forest variable importance function. Just like the random
forest variable importance function, our score handles both regression and
classification seamlessly. One of the distinct advantage of our proposed score
is the fact that it offers a natural cut off at zero, with all the positive
scores indicating importance and significance, while the negative scores are
deemed indications of insignificance. An extra advantage of our proposed score
lies in the fact it works very well beyond ensemble of trees and can seamlessly
be used with any base learners in the random subspace learning context. Our
examples, both simulated and real, demonstrate that our proposed score does
compete mostly favorably with the random forest score.
