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The effect of training data size on machine learning methods has been wellinvestigated over the past two decades. The predictive performance of treebased machine learning methods, in general, improves with a decreasing rate asthe size of training data increases. We investigate this in optimal treesensemble (OTE) where the method fails to learn from some of the trainingobservations due to internal validation. Modified tree selection methods arethus proposed for OTE to cater for the loss of training observations ininternal validation. In the first method, corresponding out-of-bag (OOB)observations are used in both individual and collective performance assessmentfor each tree. Trees are ranked based on their individual performance on theOOB observations. A certain number of top ranked trees is selected and startingfrom the most accurate tree, subsequent trees are added one by one and theirimpact is recorded by using the OOB observations left out from the bootstrapsample taken for the tree being added. A tree is selected if it improvespredictive accuracy of the ensemble. In the second approach, trees are grown onrandom subsets, taken without replacement-known as sub-bagging, of the trainingdata instead of bootstrap samples (taken with replacement). The remainingobservations from each sample are used in both individual and collectiveassessments for each corresponding tree similar to the first method. Analysison 21 benchmark datasets and simulations studies show improved performance ofthe modified methods in comparison to OTE and other state-of-the-art methods.

Optimal trees selection for classification via out-of-bag assessment and sub-bagging