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Decision tree classifiers are a widely used tool in data stream mining. Theuse of confidence intervals to estimate the gain associated with each splitleads to very effective methods, like the popular Hoeffding tree algorithm.From a statistical viewpoint, the analysis of decision tree classifiers in astreaming setting requires knowing when enough new information has beencollected to justify splitting a leaf. Although some of the issues in thestatistical analysis of Hoeffding trees have been already clarified, a generaland rigorous study of confidence intervals for splitting criteria is missing.We fill this gap by deriving accurate confidence intervals to estimate thesplitting gain in decision tree learning with respect to three criteria:entropy, Gini index, and a third index proposed by Kearns and Mansour. Ourconfidence intervals depend in a more detailed way on the tree parameters. Wealso extend our confidence analysis to a selective sampling setting, in whichthe decision tree learner adaptively decides which labels to query in thestream. We furnish theoretical guarantee bounding the probability that theclassification is non-optimal learning the decision tree via our selectivesampling strategy. Experiments on real and synthetic data in a streamingsetting show that our trees are indeed more accurate than trees with the samenumber of leaves generated by other techniques and our active learning modulepermits to save labeling cost. In addition, comparing our labeling strategywith recent methods, we show that our approach is more robust and consistentrespect all the other techniques applied to incremental decision trees.

Confidence Decision Trees via Online and Active Learning for Streaming (BIG) Data