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1. Introduction

Many researchers have investigated the technique of combining the predictions of multiple classifiers to produce a single classifier [Breiman1996a,Clemen1989,Perrone1993,Wolpert1992]. The resulting classifier (hereafter referred to as an ensemble) is generally more accurate than any of the individual classifiers making up the ensemble. Both theoretical [Hansen Salamon1990,Krogh Vedelsby1995] and empirical [Hashem1997,Opitz Shavlik1996a,Opitz Shavlik1996b] research has demonstrated that a good ensemble is one where the individual classifiers in the ensemble are both accurate and make their errors on different parts of the input space. Two popular methods for creating accurate ensembles are Bagging [Breiman1996a] and Boosting [Freund Schapire1996,Schapire1990]. These methods rely on ``resampling'' techniques to obtain different training sets for each of the classifiers. In this paper we present a comprehensive evaluation of both Bagging and Boosting on 23 data sets using two basic classification methods: decision trees and neural networks.

Previous work has demonstrated that Bagging and Boosting are very effective for decision trees [Bauer Kohavi1999,Drucker Cortes1996,Breiman1996a,Breiman1996b,Freund Schapire1996,Quinlan1996]; however, there has been little empirical testing with neural networks (especially with the new Boosting algorithm). Discussions with previous researchers reveal that many authors concentrated on decision trees due to their fast training speed and well-established default parameter settings. Neural networks present difficulties for testing both in terms of the significant processing time required and in selecting training parameters; however, we feel there are distinct advantages to including neural networks in our study. First, previous empirical studies have demonstrated that individual neural networks produce highly accurate classifiers that are sometimes more accurate than corresponding decision trees [Fisher McKusick1989,Mooney et al.1989]. Second, neural networks have been extensively applied across numerous domains [Arbib1995]. Finally, by studying neural networks in addition to decision trees we can examine how Bagging and Boosting are influenced by the learning algorithm, giving further insight into the general characteristics of these approaches. Bauer and Kohavi [1999] also study Bagging and Boosting applied to two learning methods, in their case decision trees using a variant of C4.5 and naive-Bayes classifiers, but their study mainly concentrated on the decision tree results.

Our neural network and decision tree results led us to a number of interesting conclusions. The first is that a Bagging ensemble generally produces a classifier that is more accurate than a standard classifier. Thus one should feel comfortable always Bagging their decision trees or neural networks. For Boosting, however, we note more widely varying results. For a few data sets Boosting produced dramatic reductions in error (even compared to Bagging), but for other data sets it actually increases in error over a single classifier (particularly with neural networks). In further tests we examined the effects of noise and support Freund and Schapire's [1996] conjecture that Boosting's sensitivity to noise may be partly responsible for its occasional increase in error.

An alternate baseline approach we investigated was the creation of a simple neural network ensemble where each network used the full training set and differed only in its random initial weight settings. Our results indicate that this ensemble technique is surprisingly effective, often producing results as good as Bagging. Research by Ali and Pazzani [1996] demonstrated similar results using randomized decision tree algorithms.

Our results also show that the ensemble methods are generally consistent (in terms of their effect on accuracy) when applied either to neural networks or to decision trees; however, there is little inter-correlation between neural networks and decision trees except for the Boosting methods. This suggests that some of the increases produced by Boosting are dependent on the particular characteristics of the data set rather than on the component classifier. In further tests we demonstrate that Bagging is more resilient to noise than Boosting.

Finally, we investigated the question of how many component classifiers should be used in an ensemble. Consistent with previous research [Freund Schapire1996,Quinlan1996], our results show that most of the reduction in error for ensemble methods occurs with the first few additional classifiers. With Boosting decision trees, however, relatively large gains may be seen up until about 25 classifiers.

This paper is organized as follows. In the next section we present an overview of classifier ensembles and discuss Bagging and Boosting in detail. Next we present an extensive empirical analysis of Bagging and Boosting. Following that we present future research and additional related work before concluding.

next up previous
Next: 2. Classifier Ensembles Up: Popular Ensemble Methods: An Previous: Popular Ensemble Methods: An
David Opitz