Sparse partial least squares regression for simultaneous dimension reduction and variable selection
AbstractPartial 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. Copyright Journal compilation (c) 2010 Royal Statistical Society.
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Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Volume (Year): 72 (2010)
Issue (Month): 1 ()
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- Julieta Fuentes & Pilar Poncela & Julio Rodríguez, 2014. "Selecting and combining experts from survey forecasts," Statistics and Econometrics Working Papers ws140905, Universidad Carlos III, Departamento de Estadística y Econometría.
- Julieta Fuentes & Pilar Poncela & Julio Rodríguez, 2012. "Sparse partial least squares in time series for macroeconomic forecasting," Statistics and Econometrics Working Papers ws122216, Universidad Carlos III, Departamento de Estadística y Econometría.
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