Open Access
June 2015 Estimating heterogeneous graphical models for discrete data with an application to roll call voting
Jian Guo, Jie Cheng, Elizaveta Levina, George Michailidis, Ji Zhu
Ann. Appl. Stat. 9(2): 821-848 (June 2015). DOI: 10.1214/13-AOAS700


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.


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Jian Guo. Jie Cheng. Elizaveta Levina. George Michailidis. Ji Zhu. "Estimating heterogeneous graphical models for discrete data with an application to roll call voting." Ann. Appl. Stat. 9 (2) 821 - 848, June 2015.


Received: 1 May 2013; Revised: 1 October 2013; Published: June 2015
First available in Project Euclid: 20 July 2015

zbMATH: 06499932
MathSciNet: MR3371337
Digital Object Identifier: 10.1214/13-AOAS700

Keywords: $\ell_{1}$ penalty , Binary data , graphical models , group penalty , High-dimensional data , Markov network

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.9 • No. 2 • June 2015
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