Testing significance of features by lassoed principal components

Details Testing significance of features by lassoed principal components Testing significance of features by lassoed principal components

2008-11-11

arxiv.org/abs/0811.1700v1

Annals of Applied Statistics 2008, Vol. 2, No. 3, 986-1012

Statistics

Applications

Published in at http://dx.doi.org/10.1214/08-AOAS182 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/08-AOAS182

We consider the problem of testing the significance of features in high-dimensional settings. In particular, we test for differentially-expressed genes in a microarray experiment. We wish to identify genes that are associated with some type of outcome, such as survival time or cancer type. We propose a new procedure, called Lassoed Principal Components (LPC), that builds upon existing methods and can provide a sizable improvement. For instance, in the case of two-class data, a standard (albeit simple) approach might be to compute a two-sample $t$-statistic for each gene. The LPC method involves projecting these conventional gene scores onto the eigenvectors of the gene expression data covariance matrix and then applying an $L_1$ penalty in order to de-noise the resulting projections. We present a theoretical framework under which LPC is the logical choice for identifying significant genes, and we show that LPC can provide a marked reduction in false discovery rates over the conventional methods on both real and simulated data. Moreover, this flexible procedure can be applied to a variety of types of data and can be used to improve many existing methods for the identification of significant features.

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