Augmenting the bootstrap to analyze high dimensional genomic data

Abstract

The data produced by high-throughput genomic techniques are often high dimensional and undersampled. In these settings, statistical analyses that require the inversion of covariance matrices, such as those pursuing supervised dimension reduction or the assessment of interdependence structures, are problematic. In this article we show how the idea of adding noise to the bootstrap, pioneered by Efron, and Silverman and Young, in the late seventies and eighties, can be used to overcome undersampling and effectively estimate the inverse covariance matrix for data sets in which the number of observations is small relative to the number of variables. We demonstrate the performance of this approach, which we call augmented bootstrap, on simulated data and on data derived from genomic DNA sequences and microarray experiments.