Covariate‐driven factorization by thresholding for multi‐block data

Multiblock data, where multiple groups of variables from different sources are observed for a common set of subjects, are routinely collected in many areas of science. Methods for joint factorization of such multiblock data are being developed to explore the potentially joint variation structure of the data. While most of the existing work focuses on delineating joint components, shared across all data blocks, from individual components, which is only relevant to a single data block, we propose to model and estimate partially joint components across some, but not all, data blocks. If covariates, with potential multiblock structures, are available, then the components are further modeled to be driven by the covariate information. To estimate such a covariate-driven, block-structured factor model, we propose an iterative algorithm based on thresholding, by transforming the problem of signal segmentation into a grouped variable selection problem. The proposed factorization provides accurate estimation of individual and (partially) joint structures in multiblock data, as confirmed by simulation studies. In the analysis of a real multiblock genomic dataset from the Cancer Genome Atlas project, we demonstrate that the estimated block structures provide straightforward interpretation and facilitate subsequent analyses.