Graph structure inference for high-throughput genomic data

Recent advances in high-throughput sequencing technologies enable us to study a large number of biomarkers and use their information collectively. Based on high-throughput experiments, there are many genome-wide networks constructed to characterize the complex physical or functional interactions between the biomarkers. To identify outcome-related biomarkers, it is often advantageous to make use of the known relational structure, because graph structured inference introduces smoothness and reduces complexity in modelling. In this dissertation, we propose models for high-dimensional epigenetic and genomic data that incorporate the network structure and update the network structure based on empirical evidence. In the first part of this dissertation, we propose a penalized conditional logistic regression model for high dimensional DNA methylation data. DNA methylation of CpG sites within genes are often correlated and the number of CpG sites typically far outnumbers the sample size. The new penalty function combines the truncated lasso penalty and a graph fuse-lasso penalty to induce parsimonious and consistent models, and to incorporate the CpG sites network structure without introduc