Optimal trees selection for classification via out-of-bag assessment and sub-bagging
This work offers an incremental improvement in tree-based ensemble methods for machine learning practitioners by enhancing predictive accuracy and addressing data utilization issues.
This paper addresses the issue of lost training observations in Optimal Trees Ensemble (OTE) due to internal validation, which hinders learning. The authors propose two modified tree selection methods: one using out-of-bag (OOB) observations for individual and collective tree assessment, and another employing sub-bagging instead of bootstrapping. These modifications reportedly improve performance on 21 benchmark datasets and in simulation studies compared to OTE and other state-of-the-art methods.
The effect of training data size on machine learning methods has been well investigated over the past two decades. The predictive performance of tree based machine learning methods, in general, improves with a decreasing rate as the size of training data increases. We investigate this in optimal trees ensemble (OTE) where the method fails to learn from some of the training observations due to internal validation. Modified tree selection methods are thus proposed for OTE to cater for the loss of training observations in internal validation. In the first method, corresponding out-of-bag (OOB) observations are used in both individual and collective performance assessment for each tree. Trees are ranked based on their individual performance on the OOB observations. A certain number of top ranked trees is selected and starting from the most accurate tree, subsequent trees are added one by one and their impact is recorded by using the OOB observations left out from the bootstrap sample taken for the tree being added. A tree is selected if it improves predictive accuracy of the ensemble. In the second approach, trees are grown on random subsets, taken without replacement-known as sub-bagging, of the training data instead of bootstrap samples (taken with replacement). The remaining observations from each sample are used in both individual and collective assessments for each corresponding tree similar to the first method. Analysis on 21 benchmark datasets and simulations studies show improved performance of the modified methods in comparison to OTE and other state-of-the-art methods.