bootPLS: Bootstrap hyperparameter selection for PLS models and extensions
Creators: name: Bertrand, Frederic
name: Maumy, Myriam
Publisher: name: F1000 Research Limited
Year: 2022

description: Methods based on partial least squares (PLS) regression, which has recently received much attention in the analysis of high-dimensional genomic datasets, have been developed since the early 2000s to perform variable selection. Most of these techniques rely on tuning parameters that are often determined by cross-validation (CV) based methods, which raises critical stability issues.<br> <br> To overcome this difficulty, we have recently introduced non-parametric bootstrap-based techniques for determining the number of components for regular or sparse ((s)PLS) and sparse GPLS ((s)GPLS) regression and a new dynamic bootstrap-based method for the selection of significant predictors, suitable for both PLS regression and its incorporation in generalized linear models (GPLS). These techniques rely on the establishment of bootstrap confidence intervals, which allows testing for the significance of predictors at a predefined I α risk, and avoiding CV.<br> <br> We have also developed adapted versions of sparse PLS (SPLS) and sparse GPLS regression (SGPLS), using a recently introduced non-parametric bootstrap-based technique to determine the numbers of components. We compare their variable selection reliability and stability concerning tuning parameters determination and their predictive ability, using simulated data for PLS and real microarray gene expression data for PLS-logistic classification. We observe that our new dynamic bootstrap-based method has the property of best separating random noise in y from the relevant information with respect to other methods, leading to better accuracy and predictive abilities, especially for non-negligible noise levels.<br> <br> In the PLS framework, conclusions based on our simulations are twofold. First, for datasets with negligible random noise in y, SPLS BootYT is recommended. Indeed, both in terms of accuracy and predictive abilities, it outperforms all other techniques compared here. Second, for datasets with non-negligible random noise in y, which represents the more realistic case, our new dynamic bootstrap-based method is recommended. As for SPLS BootYT for the negligible random noise variability framework, BootYTdyn outperforms all other methods for each property studied. Furthermore, it is the only method that concludes as to a decreasing number of significant predictors, while the random noise variability increases, which was expected here.<br> <br> Results obtained from our classification study using real datasets match previous conclusions. Indeed, BootYTdyn is the only one that leads to the expected PMSE values on two additional independent datasets, which allows us to suppose that over-fitting issues were avoided and that these PMSE values are induced by noise or information which cannot be modeled using only gene expression. Furthermore, the extracted probe set is already known to be linked to the relevant location in the distal colon, which strengthens our confidence in this new dynamic approach.<br> <br> Lastly, our new bootstrap-based SPLS implementation improves the stability of this method. Indeed, in all cases studied, both the SPLS CV and SGPLS CV select a higher number of unique sets of hyper-parameters than our bootstrap-based versions do, leading to higher numbers of unique supports and models too.<br> <br> The bootPLS package provides these implementations of stable bootstrap-based nonparametric techniques for determining the number of components for linear or generalized linear partial least squares regression models as well as sparse linear or generalized linear partial least squares regression models. The package brings together techniques that have been published in a book chapter (Magnanensi et al. 2016, 'The Multiple Facets of Partial Least Squares and Related Methods', ) and two articles (Magnanensi et al. 2017, 'Statistics and Computing', ) and (Magnanensi et al. 2021, 'Frontiers in Applied Mathematics and Statistics', ).