Capturing Hidden Signals From High-Dimensional Data and Applications to Genomics

The analysis of high-dimensional data, albeit challenging owing to various computational and statistical aspects, often provides opportunities to uncover hidden signals by leveraging inherent structure in the data. In the context of genomics, where molecular markers are probed at ever-increasing resolution and throughput, large sets of features that follow specific patterns, in conjunction with large sample sizes, allow us to implement richer and more sophisticated models than before in attempt to extract signal that is not immediately evident from the data. Particularly, genomic markers are often affected by multiple genetic and environmental factors, they may differ in their regulation and presentation in different tissues, cell types, conditions, or over time, and some markers may affect multiple biological processes; unveiling those signals is likely to be pivotal in advancing our understanding of complex biology and disease. This dissertation introduces novel computational methodologies and theory that address several key challenges faced in the analysis of high-dimensional genomic data coming from heterogeneous sources ("bulk" genomics) with a particular focus on DNA methylation data. Through a range of simulations and the analysis of multiple data sets, we demonstrate that our proposed methods provide opportunities to conduct powerful and statistically sound population-level studies at an unprecedented resolution and scale.