Superior feature-set ranking for small samples using bolstered error estimation

Abstract

Ranking feature sets is a key issue for classification, for instance, phenotype classification based on gene expression. Since ranking is often based on error estimation, and error estimators suffer to differing degrees of imprecision in small-sample settings, it is important to choose a computationally feasible error estimator that yields good feature-set ranking. This paper examines the feature-ranking performance of several kinds of error estimators: resubstitution, cross-validation, bootstrap and bolstered error estimation. It does so for three classification rules: linear discriminant analysis, three-nearest-neighbor classification and classification trees. Two measures of performance are considered. One counts the number of the truly best feature sets appearing among the best feature sets discovered by the error estimator and the other computes the mean absolute error between the top ranks of the truly best feature sets and their ranks as given by the error estimator. Our results indicate that bolstering is superior to bootstrap, and bootstrap is better than cross-validation, for discovering top-performing feature sets for classification when using small samples. A key issue is that bolstered error estimation is tens of times faster than bootstrap, and faster than cross-validation, and is therefore feasible for feature-set ranking when the number of feature sets is extremely large.