Sparse partial least squares regression for simultaneous dimension reduction and variable selection

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency...

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Veröffentlicht in:	Journal of the Royal Statistical Society. Series B, Statistical methodology Jg. 72; H. 1; S. 3 - 25
Hauptverfasser:	Chun, Hyonho, Keleş, Sündüz
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Oxford, UK Oxford, UK : Blackwell Publishing Ltd 2010 Blackwell Publishing Ltd Wiley-Blackwell Blackwell Royal Statistical Society Oxford University Press
Schriftenreihe:	Journal of the Royal Statistical Society Series B
Schlagworte:	Attention Biostatistics Chromatin immuno-precipitation Consistent estimators Data Dimension reduction Dimensionality reduction Direction vectors Estimators Exact sciences and technology Experiments Gene expression General topics Genomics Lasso Least squares Least squares method Linear inference, regression Linear regression Mathematical vectors Mathematics Matrices Microarrays Multivariate analysis Original Paradigms Partial least squares Probability and statistics Regression analysis Sample size Sciences and techniques of general use Simulation Sparsity Statistical methods Statistics Studies Threshing Variable and feature selection Chromatin immuno-precipitation Microarrays Lasso Multivariate regression Regression analysis Microarray Gene expression Asymptotic convergence Implementation Statistical method Statistical regression Dimension reduction Linear combination Simulation Sparsity Least squares method Variable and feature selection Partial least squares Variable selection
ISSN:	1369-7412, 1467-9868
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Zusammenfassung:	Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data.
Bibliographie:	http://dx.doi.org/10.1111/j.1467-9868.2009.00723.x istex:BCCB099C8A57A2A8A4CC0C5D6685E2643AF997E1 ArticleID:RSSB723 ark:/67375/WNG-6Z5274M3-M Reuse of this article is permitted in accordance with the terms and conditions set out at http://www3.interscience.wiley.com/authorresources/onlineopen.html . SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2 Reuse of this article is permitted in accordance with the terms and conditions set out at http://www3.interscience.wiley.com/authorresources/onlineopen.html.
ISSN:	1369-7412 1467-9868
DOI:	10.1111/j.1467-9868.2009.00723.x