Title
Ensemble Methods Based on Optimal Selection and Addition of Classifiers

Authors

Faisal M. Zaman


Source
BHƑww@Hw@Ȋwm_iHwAHbQSXj, pp. 1-100 (2011.1.11)

Abstract
To improve the prediction accuracy of a prediction problem, it is prevalent to combine multiple versions of a prediction algorithm rather than improving the accuracy of the single algorithm. This method of combining the predictions of multiple versions of a single algorithm over a single prob- lem is known as ensemble learning. Ensemble learning methods have been a major area of research of various disciplines such as statistical datamining, pattern recognition, and machine learning. An ensemble method is constructed in two ways; either by training the component classifiers parallelly or by training the component classifiers sequentially. In this thesis,our main focus is on parallel ensemble methods.
The success of the ensemble methods is analyzed from several viewpoints. First, it is is from a maximum margin classifier viewpoint. In this approach, it is shown that an ensemble classifier method maximizes the margin of the classifier, improving the generalizing ability of the classifier. The other is from the classical bias-variance decomposition theory of the misclassification error; it is shown that ensemble methods reduce bias-variance of the classifier and finally a better gener- alization ability. Besides these two approaches to decipher the mechanism of ensemble methods, there is another approach, which is concerned about the stability of the component algorithm of an ensemble. In this approach, it is shown that an ensemble method is only effective if the ensem- ble method is more stable than a component of classifiers of the ensemble, which approximately means that the generalization ability goes up. Following this approach, it is not feasible to construct any conventional ensemble methods (more specifically the parallel ensemble methods) with stable component classifiers. However, the main advantage of the stable classifiers over their unstable counterpart is that the variance of the stable one is lower than the unstable one.
In this thesis, our main objective is to construct efficient parallel ensemble methods using the stable classifiers, exploiting its low variance property. For this purpose, we propose two ensemble designs to utilize the stable classifiers. The first design is in accordance with the third approach mentioned above. In this design, we propose to control the stability of the component classifiers, so that the constructed ensemble gains superior to the generalization ability when they are aggregated (combined). In this type of ensemble, we have inserted an additional selection/validation step to select or validate the component stable classifiers having a certain limit of generalization ability. Then, the selected classifiers are combined using robust statistics, so that the final ensemble is resistant to any unusual output of any of the component classifiers. The next design is in accordance with the second approach stated above. In this design, we propose to enlarge the feature space of the component base classifiers, so that bias-variance of the constructed ensemble is reduced simultaneously. In this type of ensemble, we increase the representational power of the component base classifiers by adding extra features from the outcome of additional stable classifiers; in this way, the bias can be reduced, and by the constitutional steps of the underlying parallel ensemble method, the variance is also reduced. In both of our ensemble designs, to validate/select and add the outcomes from stable classifier we have used samples, which are independent of the training resamples (these training resamples are defined as inbag sample).
These samples are built-in samples with the inbag samples and are defined as Out-of-bag samples (OOBS). The main advantage of using these samples in designing our ensembles is that, the in- stances of these samples are discarded from its inbag resample part; so the validation process is optimum and the added features from the stable classifiers are also near optimum.

Key Words
Out-of-Bag samples, Stable classifier, Parallel ensemble method, Resampling with and without replacement

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