Model Selection in Undirected Graphical Models with the Elastic Net

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associated with a Gaussian Markov Random Field (GMRF), the Ising model and the Potts model, by extending previous work on $l_1$ regularized neighborhood estimation to include the elastic net $l_1+l_2$ penalty. Additionally, we show numerical evidence that the edge density plays a role in the graph recovery process. Finally, we introduce a novel method for augmenting neighborhood estimation by leveraging pair-wise neighborhood union estimates.