Ensembles of Restricted Hoeffding Trees

The success of simple methods for classification shows that is is often not necessary to model complex attribute interactions to obtain good classification accuracy on practical problems. In this article, we propose to exploit this phenomenon in the data stream context by building an ensemble of Hoeffding trees that are each limited to a small subset of attributes. In this way, each tree is restricted to model interactions between attributes in its corresponding subset. Because it is not known a priori which attribute subsets are relevant for prediction, we build exhaustive ensembles that consider all possible attribute subsets of a given size. As the resulting Hoeffding trees are not all equally important, we weigh them in a suitable manner to obtain accurate classifications. This is done by combining the log-odds of their probability estimates using sigmoid perceptrons, with one perceptron per class. We propose a mechanism for setting the perceptrons’ learning rate using the change detection method for data streams, and also use to reset ensemble members (i.e., Hoeffding trees) when they no longer perform well. Our experiments show that the resulting ensemble classifier outperforms bagging for data streams in terms of accuracy when both are used in conjunction with adaptive naive Bayes Hoeffding trees, at the expense of runtime and memory consumption. We also show that our stacking method can improve the performance of a bagged ensemble.