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An information theoretic approach to learning the complexity ofclassification and regression trees and the number of trees in gradient treeboosting is proposed. The optimism (test loss minus training loss) of thegreedy leaf splitting procedure is shown to be the maximum of aCox-Ingersoll-Ross process, from which a generalization-error based informationcriterion is formed. The proposed procedure allows fast local model selectionwithout cross validation based hyper parameter tuning, and hence efficient andautomatic comparison among the large number of models performed during eachboosting iteration. Relative to xgboost, speedups on numerical experimentsranges from around 10 to about 1400, at similar predictive-power measured interms of test-loss.

An information criterion for automatic gradient tree boosting