title: ESTIMATING HETEROGENEOUS GRAPHICAL MODELS FOR DISCRETE DATA WITH AN APPLICATION TO ROLL CALL VOTING.
abstract: We consider the problem of jointly estimating a collection of graphical models for discrete data, corresponding to several categories that share some common structure. An example for such a setting is voting records of legislators on different issues, such as defense, energy, and healthcare. We develop a Markov graphical model to characterize the heterogeneous dependence structures arising from such data. The model is fitted via a joint estimation method that preserves the underlying common graph structure, but also allows for differences between the networks. The method employs a group penalty that targets the common zero interaction effects across all the networks. We apply the method to describe the internal networks of the U.S. Senate on several important issues. Our analysis reveals individual structure for each issue, distinct from the underlying well-known bipartisan structure common to all categories which we are able to extract separately. We also establish consistency of the proposed method both for parameter estimation and model selection, and evaluate its numerical performance on a number of simulated examples.
authors.affiliation: Department of Biostatistics, Harvard University, 655 Huntington Avenue, Boston, Massachusetts 02115, USA.
authors.forename: Jian
authors.initials: J
authors.lastname: Guo
authors.affiliation: Department of Statistics, University of Michigan, 1085 South University, Ann Arbor, Michigan 48109-1107, USA.
authors.forename: Jie
authors.initials: J
authors.lastname: Cheng
authors.affiliation: Department of Statistics, University of Michigan, 1085 South University, Ann Arbor, Michigan 48109-1107, USA.
authors.forename: Elizaveta
authors.initials: E
authors.lastname: Levina
authors.affiliation: Department of Statistics, University of Michigan, 1085 South University, Ann Arbor, Michigan 48109-1107, USA.
authors.forename: George
authors.initials: G
authors.lastname: Michailidis
authors.affiliation: Department of Statistics, University of Michigan, 1085 South University, Ann Arbor, Michigan 48109-1107, USA.
authors.forename: Ji
authors.initials: J
authors.lastname: Zhu
keywords: Graphical models; Markov network; binary data; group penalty; high-dimensional data; ℓ1 penalty