GfKl 2008 - Legos

Classification of Paired Data Using Ensemble
Methods
Werner Adler 1 , Alexander Brenning 2 , and Berthold Lausen 1
1
Chair for Biometry and Epidemiology, University of Erlangen-Nuremberg,
Germany
werner.adler@imbe.imed.uni-erlangen.de,
berthold.lausen@rzmail.uni-erlangen.de
2
Department of Geography, University of Waterloo, Canada
brenning@fesmail.uwaterloo.ca
Abstract. In glaucoma classification, the underlying data have a paired structure
that often is accounted for by simply using only one eye per subject. Brenning and
Lausen (2008) showed that the proper use of both eyes in paired cross-validation
decreases the variance of the estimation, compaired to cross-validation using only
one eye per subject.
We discuss and compare different strategies to generate the bootstrap samples
for training Adaboost (Freund and Schapire, 1996), Random Forest (Breiman, 2001),
and Double Bagging (Hothorn and Lausen, 2005). The simplest approach is to ignore
the paired data structure and proceed as usual. Adapting the idea by Brenning and
Lausen, we also perform subject based sampling. In a first step, subjects are drawn
with replacement. In a second step, for each drawn subject either both eyes or
one randomly selected eye are chosen, or two eyes are drawn with replacement.
The subjects not selected for training the base learners constitute the out-of-bag
samples. We compare error rates resulting from these different approaches obtained
by a simulation study.
Key words: Bootstrap, Classification, Glaucoma, Paired Organs
References
Breiman, L. (2001): Random forests. Machine Learning, 45, 5–32.
Brenning, A. and Lausen, B. (2008): Estimating error rates in the classification of
paired organs. Statistics in Medicine, submitted.
Freund, Y. and Schapire, R. (1996): Experiments with a new boosting algorithm.
Proceedings of the 13th International Conference on Machine Learning, 148–
156.
Hothorn, T. and Lausen, B. (2005): Bundling classifiers by bagging trees. Computational
Statistics & Data Analysis, 49, 1068–1078.
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