Transfer learning for sparse multivariate principal covariates regression

In high-dimensional, small-sample settings, traditional principal covariate regression often suffers from overfitting and limited interpretability. To address these issues, we propose Transfer Learning for Sparse Multivariate Principal Covariates Regression (Trans-SMPCovR), which integrates transfer learning with sparse variable selection, and develop two variants: an idealized Oracle Trans-SMPCovR for settings with known informative auxiliary domains and a practical Trans-SMPCovR with relevance-aware screening for settings in which auxiliary-domain informativeness is unknown. Under the representative high-dimensional, small-sample simulation settings considered here, both transfer-learning-based methods improve predictive performance and structural recovery relative to the no-transfer baseline, with substantial gains in prediction accuracy and marked improvement in Tucker congruence; paired comparisons and bootstrap confidence intervals further support these improvements. Additional heterogeneity-gradient experiments show that Oracle Trans-SMPCovR performs best when auxiliary domains are highly similar to the target domain, whereas Trans-SMPCovR is more robust as cross-domain heterogeneity increases. In the Pittsburgh Common Cold Study, Trans-SMPCovR outperforms the no-transfer baseline, while the Oracle version is more sensitive to domain mismatch. These results suggest that Trans-SMPCovR provides a practical and robust framework for high-dimensional, small-sample, multi-source data analysis.