High dimensional classifiers in the imbalanced case

A binary classification problem is imbalanced when the number of samples from the two groups differs. For the high dimensional case, where the number of variables is much larger than the number of samples, imbalance leads to a bias in the classification. The independence classifier is studied theoretically and based on the analysis two new classifiers are suggested that can handle any imbalance ratio. The analytical results are supplemented by a simulation study, where the suggested classifiers in some aspects outperform multiple undersampling. For correlated data the ROAD classifier is considered and a suggestion is given for how to modify the classifier to handle the bias from imbalanced group sizes.