Thursday, November 5, 2015 - 3:00pm
Cockins Hall (CH), Room 240
Mixed Graphical Models with Applications to Integrative Genomics
Genevera Allen, Rice University
"Mixed Data'' comprising a large number of heterogeneous variables (e.g. count, binary, continuous, skewed continuous, among others) is prevalent in varied areas such as imaging genetics, national security, social networking, Internet advertising, and our particular motivation - high-throughput integrative genomics. There have been limited efforts at statistically modeling such mixed data jointly. In this talk, we address this by introducing several new classes of Markov Random Fields (MRFs), or graphical models, that yield joint densities which directly parameterize dependencies over mixed variables. To begin, we present a novel class of MRFs arising when all node-conditional distributions follow univariate exponential family distributions that, for instance, yield novel Poisson graphical models. Next, we present several new classes of Mixed MRF distributions built by assuming each node-conditional distribution follows a potentially different exponential family distribution. Fitting these models and using them to select the mixed graph in high-dimensional settings can be achieved via penalized conditional likelihood estimation that comes with strong statistical guarantees. Simulations as well as an application to integrative cancer genomics demonstrate the versatility of our methods.
Joint work with Eunho Yang, Pradeep Raviukmar, Zhandong Liu, Yulia Baker and Ying-Wooi Wan