Speaker:  Yunhui Qi, PhD Candidate, Department of Statistics, Iowa State University

Title: Contrastive Eigenanalysis for Exploring Hidden Effects.

Abstract: Contrastive principal component analysis (cPCA) and its sparse version (scPCA) have been effectively applied to identify treatment-enriched latent subgroups. However, the theoretical understanding of subgroup detection remains unclear. In addition, the tuning parameter required in the application of cPCA and scPCA has not been well studied, and there are no available methods that allow the automatic selection of the tuning parameter. More importantly, few statistical methods have been developed for contrastive analysis of multi-modal data. In this paper, we introduce a comprehensive contrastive eigenanalysis framework by employing singular value decomposition and penalized matrix decomposition. Within this framework, we analyze cPCA to unveil the conditions for subgroup identification and nuisance effects removal. We theoretically derive the optimal tuning parameter values for subgroup identification and propose an algorithm for selecting the tuning parameter in practice. Furthermore, we introduce two innovative approaches, contrastive cross-covariance analysis (3CA) and its sparse version (s3CA), for examining changes in cross-modal data relationships from control to treatment groups. Theoretical analysis proves the adaptability of these methods in managing various error covariances and in distinguishing between shared and unique factors. We demonstrate via simulation studies that our methods show promising performances. We apply scPCA to a gene expression dataset and s3CA to a COVID-19 multi-omics dataset, providing insights into biological systems with contrastive analysis.