# Mixed Graphical Models via Exponential Families

#### Eunho Yang, Yulia Baker, Pradeep Ravikumar, Genevera Allen, Zhandong Liu

Abstract:   Markov Random Fields, or undirected graphical models are widely used to model high-dimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions citep{YRAL12} to graphical models specified by univariate exponential families, assume all variables arise from the same distribution. Complex data from high-throughput genomics and social networking for example, often contain discrete, count, and continuous variables measured on the same set of samples. To model such heterogeneous data, we develop a novel class of mixed graphical models by specifying that each node-conditional distribution is a member of a possibly different univariate exponential family. We study several instances of our model, and propose scalable $M$-estimators for recovering the underlying network structure. Simulations as well as an application to learning mixed genomic networks from next generation sequencing and mutation data demonstrate the versatility of our methods.