Open AccessTESTING SIGNIFICANCE OF FEATURES BY LASSOED PRINCIPAL COMPONENTS.
Author(s) -
Daniela Witten,
Robert Tibshirani
Publication year - 2008
Publication title -
pubmed
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.674
H-Index - 75
pISSN - 1932-6157
DOI - 10.1214/08-aoas182supp
Subject(s) - computer science , principal component analysis , test statistic , type i and type ii errors , statistical hypothesis testing , statistic , false discovery rate , covariance , identification (biology) , sample size determination , pattern recognition (psychology) , noise (video) , covariance matrix , multiple comparisons problem , data mining , artificial intelligence , algorithm , mathematics , statistics , gene , biology , genetics , botany , image (mathematics)
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.