Correcting the optimal resampling-based error rate by estimating the error rate of wrapper algorithms

High-dimensional binary classification tasks, for example, the classification of microarray samples into normal and cancer tissues, usually involve a tuning parameter. By reporting the performance of the best tuning parameter value only, over-optimistic prediction errors are obtained. For correcting this tuning bias, we develop a new method which is based on a decomposition of the unconditional error rate involving the tuning procedure, that is, we estimate the error rate of wrapper algorithms as introduced in the context of internal cross-validation (ICV) by Varma and Simon (2006, BMC Bioinformatics 7, 91). Our subsampling-based estimator can be written as a weighted mean of the errors obtained using the different tuning parameter values, and thus can be interpreted as a smooth version of ICV, which is the standard approach for avoiding tuning bias. In contrast to ICV, our method guarantees intuitive bounds for the corrected error. Additionally, we suggest to use bias correction methods also to address the conceptually similar method selection bias that results from the optimal choice of the classification method itself when evaluating several methods successively. We demonstrate the performance of our method on microarray and simulated data and compare it to ICV. This study suggests that our approach yields competitive estimates at a much lower computational price.