This article is a study of techniques for bias reduction of estimates of risk both globally and within terminal nodes of CARTR classification trees. In Section 5.4 of Classification and Regression Trees, Leo Breiman presented an estimator that has two free parameters. An empirical Bayes method was put forth for estimating them. Here we explain why the estimator should be successful in the many examples for which it is. We give numerical evidence from simulations in the two-class case with attention to ordinary resubstitution and seven other methods of estimation. There are 14 sampling distributions, all but one simulated and the remaining concerning E. coli promoter regions. We report on varying minimum node sizes of the trees; prior probabilities and misclassification costs; and, when relevant, the numbers of bootstraps or cross-validations. A variation of Breiman's method in which repeated cross-validation is employed to estimate global rates of misclassification was the most accurate from among the eight methods. Exceptions are cases for which the Bayes risk of the Bayes rule is small. For them, either a local bootstrap .632 estimate or Breiman's method modified to use a bootstrap estimate of the global misclassification rate is most accurate.
The design of a pattern recognition system requires careful attention to error estimation. The error rate is the most important descriptor of a classifier's performance. The com...
Breiman's bagging and Freund and Schapire's boosting are recent methods for improving the predictive power of classifier learning systems. Both form a set of classifiers that ar...
The term "bias" is widely used---and with different meanings---in the fields of machine learning and statistics. This paper clarifies the uses of this term and...
Recently there has been a lot of interest in “ensemble learning” — methods that generate many classifiers and aggregate their results. Two well-known methods are boosting (see, ...
In the context of cancer diagnosis and treatment, we consider the problem of constructing an accurate prediction rule on the basis of a relatively small number of tumor tissue s...
Social media, news, blog, policy document mentions