Allen, Genevera I2019-05-162019-05-162017-082017-10-06August 201Baker, Yulia. "Methods and Applications for Mixed Graphical Models." (2017) Diss., Rice University. <a href="https://hdl.handle.net/1911/105527">https://hdl.handle.net/1911/105527</a>.https://hdl.handle.net/1911/105527``Multi-view Data'' is a term used to describe heterogeneous data measured on the same set of observations but collected from different sources and of potentially different types (continuous, discrete, count). This type of data is prevalent in various fields, such as imaging genetics, national security, social networking, Internet advertising, and our particular motivation - high-throughput integrative genomics. There have been limited efforts directed at statistically modeling such mixed data jointly. In this thesis, we address this by introducing a novel class of Mixed Markov Random Field (MRFs) and Mixed Chain Markov Random Field distributions, or graphical models. Mixed MRFs assume that each node-conditional distribution arises from a different exponential family model. And Mixed Chain MRFs incorporate directed and undirected edges, in addition to different exponential family models, to produce more flexible models with less restrictive normalizibility constraints. Mixed MRFs and Mixed Chain MRFS, both yield joint densities, which can directly parameterize dependencies over mixed variables. Fitting these models to perform mixed graph selection entails estimating penalized generalized linear models with mixed covariates. Model selection with mixed covariates in a high dimensional setting, however, poses many challenges due to differences in the scale and potential signal interference between variables. In this thesis, we introduce this novel class of Mixed MRFs and Mixed Chain MRFs, study model estimation challenges theoretically and empirically, and propose a new iterative block estimation strategy. Our methods are applied to infer a gene regulatory network in three ovarian cancer studies that integrate methylation, micro-RNA expression, mutation, and gene expression data to fully understand regulatory relationships in ovarian cancer.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Multi-view Datamixed graphical modelsMarkov Random Fieldsmodel selectiongene regulatory networkThesis2019-05-16