Cooperative Learning with Penalized Linear Mixed-Effects Models for High-Dimensional Clustered Multiview Data

In biomedical research, multiple types of high-dimensional data, such as genomic, transcriptomic, proteomic, and metabolomic data, are increasingly collected from the same subjects. Integrating these multiple data views can improve prediction by exploiting shared or complementary information across the views. Cooperative learning provides an agreement-based framework for multiview supervised learning by encouraging predictions obtained from individual views to be similar. However, the original framework assumes independent observations and therefore does not account for clustered structures, such as repeated measurements obtained from the same subject. To address this limitation, we propose Cooperative Learning with a penalized Linear Mixed Model (CL-pLMM) for high-dimensional multiview data with a clustered structure. CL-pLMM replaces the ordinary prediction loss in cooperative learning with a covariance-weighted loss that accounts for within-cluster dependence, while retaining the agreement penalty between views and a Lasso penalty for variable selection. We further show that its objective function can be represented as a penalized linear mixed-effects model applied to augmented data, allowing existing estimation procedures to be used. The performance of CL-pLMM is evaluated through simulation studies under various signal and dependence settings and an application to longitudinal proteomic and metabolomic data for predicting the time to spontaneous labor.