A Naive-Bayes approach to Bolstered error estimation in high-dimensional spaces

Abstract

Bolstered error estimation has been shown to perform better than cross-validation and competitively with bootstrap in small-sample settings. However, its performance can deteriorate in the high-dimensional settings prevalent in Genomic Signal Processing. We propose here a modification of Bolstered error estimation that is based on the principle of Naive Bayes. Rather than attempting to estimate a single variance parameter for a spherical bolstering kernel in high-dimensional spaces from a small sample, we assume an ellipsoidal kernel and estimate each univariate variance separately along each variable. In simulation results based on a model for gene-expression data and a linear SVM classification rule, the new bolstered estimator clearly outperformed the old one, as well as cross-validation and resubstitution, and was also superior to the 0.632 bootstrap except in the case where a large feature set is selected.