A Unified Regularized Group PLS Algorithm Scalable to Big Data. Application on Genomics Data

摘要

Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of observations and in presence of high collinearity between variables. Different sparse versions of PLS have been developed to integrate multiple data sets while simultaneously selecting the contributing variables. Sparse modelling is a key factor in obtaining better estimators and identifying associations between multiple data sets. The cornerstone of the sparsity version of PLS methods is the link between the SVD of a matrix (constructed from deflated versions of the original matrices of data) and least squares minimisation in linear regression. We present here an accurate description of the most popular PLS methods, alongside their mathematical proofs. A unified algorithm is proposed to perform all four types of PLS including their regularised versions. Our methods enable us to identify important relationships between genomic expression and cytokine data from an HIV vaccination trial. We also proposed a new methodology by accounting for both grouping of genetic markers (e.g. genesets) and temporal effects. Finally, various approaches to decrease the computation time are offered, and we show how the whole procedure can be scalable to big data sets.