  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.
