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6. Conclusions

This paper presents a comprehensive empirical evaluation of Bagging and Boosting for neural networks and decision trees. Our results demonstrate that a Bagging ensemble nearly always outperforms a single classifier. Our results also show that a Boosting ensemble can greatly outperform both Bagging and a single classifier. However, for some data sets Boosting may show zero gain or even a decrease in performance from a single classifier. Further tests indicate that Boosting may suffer from overfitting in the presence of noise which may explain some of the decreases in performance for Boosting. We also found that a simple ensemble approach of using neural networks that differ only in their random initial weight settings performed surprisingly well, often doing as well as the Bagging.

Analysis of our results suggests that the performance of both Boosting methods (Ada-Boosting and Arcing) is at least partly dependent on the data set being examined, where Bagging shows much less correlation. The strong correlations for Boosting may be partially explained by its sensitivity to noise, a claim supported by additional tests. Finally, we show that much of the performance enhancement for an ensemble comes with the first few classifiers combined, but that Boosting decision trees may continue to further improve with larger ensemble sizes.

In conclusion, as a general technique for decision trees and neural networks, Bagging is probably appropriate for most problems, but when appropriate, Boosting (either Arcing or Ada) may produce larger gains in accuracy.

Acknowledgments

This research was partially supported by University of Minnesota Grants-in-Aid to both authors. Dave Opitz was also supported by National Science Foundation grant IRI-9734419, the Montana DOE/EPSCoR Petroleum Reservoir Characterization Project, a MONTS grant supported by the University of Montana, and a Montana Science Technology Alliance grant. This is an extended version of a paper published in the Fourteenth National Conference on Artificial Intelligence.


next up previous
Next: Bibliography Up: Popular Ensemble Methods: An Previous: 5. Additional Related Work
David Opitz
1999-08-24