Journal
ANNALS OF APPLIED STATISTICS
Volume 9, Issue 2, Pages 821-848Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/13-AOAS700
Keywords
Graphical models; group penalty; high-dimensional data; l(1) penalty; Markov network; binary data
Categories
Funding
- NSF [DMS-01-106772, DMS-11-59005, DMS-12-28164, DMS-07-05532, DMS-07-48389]
- NIH [1RC1CA145444-0110]
- Direct For Mathematical & Physical Scien [1228164] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1545277, 1106772] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1228164] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1407698, 1159005] Funding Source: National Science Foundation
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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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