Sparse Covariate Dependent Binary Markov Networks

• Activity Number: 465
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jie Cheng*+ and Ji Zhu and Liza Levina
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: binary markov network ; sparse ; conditional likelihood ; regularized logistic regression ; gene network

Abstract

Motivated by the availability of informative covariates or features when modeling the network structure for multivariate binary data, we propose a sparse covariate dependent Ising model to study the conditional dependency patterns of the binary variables and their relationship with the covariates. Our model relaxes the i.i.d. assumption of the network data commonly used in the literature and naturally incorporates the covariate information to produce subject-specific graphical models. Assuming both the underlying graphs and the effective covariates for each edge being sparse, we propose two approaches with $l_1$ regularization to fit the model. One is based on neighborhood selection and the other on pseudo likelihood. Asymptotic results are established for the estimates. We design several sets of simulation studies to illustrate the patterns of selection performance using the proposed methods. We conclude with an application of our model on a genomic instability data from tumor samples.