Improving on Bagging with Input Smearing

Abstract

Bagging is an ensemble learning method that has proved to be a useful tool in the arsenal of machine learning practitioners. Commonly applied in conjunction with decision tree learners to build an ensemble of decision trees, it often leads to reduced errors in the predictions when compared to using a single tree. A single tree is built from a training set of size N. Bagging is based on the idea that, ideally, we would like to eliminate the variance due to a particular training set by combining trees built from all training sets of size N. However, in practice, only one training set is available, and bagging simulates this platonic method by sampling with replacement from the original training data to form new training sets. In this paper we pursue the idea of sampling from a kernel density estimator of the underlying distribution to form new training sets, in addition to sampling from the data itself. This can be viewed as “smearing out” the resampled training data to generate new datasets, and the amount of “smear” is controlled by a parameter. We show that the resulting method, called “input smearing”, can lead to improved results when compared to bagging. We present results for both classification and regression problems.