  We develop scalable randomized kernel methods for jointly associating data
from multiple sources and simultaneously predicting an outcome or classifying a
unit into one of two or more classes. The proposed methods model nonlinear
relationships in multiview data together with predicting a clinical outcome and
are capable of identifying 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. Through
simulation studies, we show that the proposed methods outperform several other
linear and nonlinear methods for multiview data integration. When the proposed
methods were applied to gene expression, metabolomics, proteomics, and
lipidomics data pertaining to COVID-19, we identified several molecular
signatures forCOVID-19 status and severity. Results from our real data
application and simulations with small sample sizes suggest that the proposed
methods may be useful for small sample size problems. Availability: Our
algorithms are implemented in Pytorch and interfaced in R and would be made
available at: https://github.com/lasandrall/RandMVLearn.
