Scalable randomized kernel methods for multiview data integration and prediction with application to Coronavirus disease

There is still more to learn about the pathobiology of coronavirus disease (COVID-19) despite 4 years of the pandemic. A multiomics approach offers a comprehensive view of the disease and has the potential to yield deeper insight into the pathogenesis of the disease. Previous multiomics integrative analysis and prediction studies for COVID-19 severity and status have assumed simple relationships (ie linear relationships) between omics data and between omics and COVID-19 outcomes. However, these linear methods do not account for the inherent underlying nonlinear structure associated with these different types of data. The motivation behind this work is to model nonlinear relationships in multiomics and COVID-19 outcomes, and to determine key multidimensional molecules associated with the disease. Toward this goal, we develop scalable randomized kernel methods for jointly associating data from multiple sources or views and simultaneously predicting an outcome or classifying a unit into one of 2 or more classes. We also determine variables or groups of variables that best contribute to the relationships among the views. We use the idea that random Fourier bases can approximate shift-invariant kernel functions to construct nonlinear mappings of each view and we use these mappings and the outcome variable to learn view-independent low-dimensional representations. We demonstrate the effectiveness of the proposed methods through extensive simulations. When the proposed methods were applied to gene expression, metabolomics, proteomics, and lipidomics data pertaining to COVID-19, we identified several molecular signatures for COVID-19 status and severity. Our results agree with previous findings and suggest potential avenues for future research. Our algorithms are implemented in Pytorch and interfaced in R and available at: https://github.com/lasandrall/RandMVLearn.