Statistical Methods for Structure Discovery in Genomic and Clinical Data

Statistical analysis of modern biomedical data requires methods capable of handling high dimensionality, complex dependence structures, and evolving biological systems. This dissertation develops statistical methodologies for two important classes of biomedical data: alternative polyadenylation (APA) measurements from transcriptomic studies and longitudinal discrete event data from electronic health records.

The first part of the dissertation focuses on transcript-aware analysis of APA, a widespread post-transcriptional regulatory mechanism. Existing approaches often struggle to accurately identify polyadenylation sites and to determine whether APA usage depends on biological variables after accounting for some explanatory biological variables. To address these challenges, I develop a unified framework that incorporates transcript structure into peak identification and polyadenylation-site annotation and formulates APA analysis as a conditional independence testing problem. 

The second part of the dissertation develops H-DOGTOR, a framework for dynamic knowledge graph learning from longitudinal discrete event data. H-DOGTOR models event occurrences using multivariate Hawkes processes whose baseline intensities and interaction networks vary smoothly across external environments. To address high dimensionality, the framework incorporates both sparsity and low-rank structural constraints, enabling recovery of localized interactions and latent network structure.

Together, these methodologies provide statistically rigorous tools for learning biological structure and dependence from complex biomedical data. By integrating machine learning, high-dimensional inference, and stochastic process modeling, this work advances both transcriptomic regulation analysis and dynamic clinical knowledge discovery.