Boosting for high-dimensional two-class prediction

Rok Blagus, Lara Lusa

In clinical research prediction models are used to accurately predict the outcome of the patients based on some of their characteristics. For high-dimensional prediction models (the number of variables greatly exceeds the number of samples) the choice of an appropriate classifier is crucial as it was observed that no single classification algorithm performs optimally for all types of data. Boosting was proposed as a method that combines the classification results obtained using base classifiers, where the sample weights are sequentially adjusted based on the performance in previous iterations. Generally boosting outperforms any individual classifier, but studies with high-dimensional data showed that the most standard boosting algorithm, AdaBoost.M1, cannot significantly improve the performance of its base classier. Recently other boosting algorithms were proposed (Gradient boosting, Stochastic Gradient boosting, LogitBoost); they were shown to perform better than AdaBoost.M1 but their performance was not evaluated for high-dimensional data. In this paper we use simulation studies and real gene-expression data sets to evaluate the performance of boosting algorithms when data are high-dimensional. Our results confirm that AdaBoost.M1 can perform poorly in this setting, often failing to improve the performance of its base classifier. We provide the explanation for this and propose a modification, AdaBoost.M1.ICV, which uses cross-validated estimates of the prediction errors and outperforms the original algorithm when data are high-dimensional. The use of AdaBoost.M1.ICV is advisable when the base classifier overfits the training data: the number of variables is large, the number of samples is small, and/or the difference between the classes is large. To a lesser extent also Gradient boosting suffers from similar problems. Contrary to the findings for the low-dimensional data, shrinkage does not improve the performance of Gradient boosting when data are high-dimensional, however it is beneficial for Stochastic Gradient boosting, which outperformed the other boosting algorithms in our analyses. LogitBoost suffers from overfitting and generally performs poorly. The results show that boosting can substantially improve the performance of its base classifier also when data are high-dimensional. However, not all boosting algorithms perform equally well. LogitBoost, AdaBoost.M1 and Gradient boosting seem less useful for this type of data. Overall, Stochastic Gradient boosting with shrinkage and AdaBoost.M1.ICV seem to be the preferable choices for high-dimensional class-prediction.