2010
DOI: 10.1111/j.1467-9868.2009.00723.x
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Sparse Partial Least Squares Regression for Simultaneous Dimension Reduction and Variable Selection

Abstract: 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 square… Show more

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Cited by 723 publications
(709 citation statements)
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“…The model obtained is complex since new variables are represented in a new dimensional space [37]. The SPLS-DA is based in the sparsity principle [38], on the basis that not all explanatory variables are needed to the fit model, i.e., meaning that a subset of original variables could be mainly responsible for determining the response. Therefore, SPLS-DA also has the ability to perform feature selection keeping the structure of PLS-DA model.…”
Section: Discussionmentioning
confidence: 99%
“…The model obtained is complex since new variables are represented in a new dimensional space [37]. The SPLS-DA is based in the sparsity principle [38], on the basis that not all explanatory variables are needed to the fit model, i.e., meaning that a subset of original variables could be mainly responsible for determining the response. Therefore, SPLS-DA also has the ability to perform feature selection keeping the structure of PLS-DA model.…”
Section: Discussionmentioning
confidence: 99%
“…However, using sparse PLSR (Chun and Keles, 2010) instead of conventional PLSR could remedy this. Moreover, given the current state of the hardware this is not a problem for off-line analysis and model improvements.…”
Section: Resultsmentioning
confidence: 99%
“…Through a large, pre-determined number of repeated samplings with replacements, the distribution parameters of coefficients were estimated, and their confidence intervals (CI) were calculated. Features that did not pass the significance test were removed [46].…”
Section: Resultsmentioning
confidence: 99%