Learning Graphical Models With Hubs
This work addresses the need for more realistic network modeling in domains like webpage and gene expression analysis, but it is incremental as it builds on existing l1 penalty methods.
The authors tackled the problem of learning high-dimensional graphical models with hub nodes, which are highly-connected, by proposing a convex framework using a row-column overlap norm penalty, and demonstrated that it outperforms competitors on synthetic data.
We consider the problem of learning a high-dimensional graphical model in which certain hub nodes are highly-connected to many other nodes. Many authors have studied the use of an l1 penalty in order to learn a sparse graph in high-dimensional setting. However, the l1 penalty implicitly assumes that each edge is equally likely and independent of all other edges. We propose a general framework to accommodate more realistic networks with hub nodes, using a convex formulation that involves a row-column overlap norm penalty. We apply this general framework to three widely-used probabilistic graphical models: the Gaussian graphical model, the covariance graph model, and the binary Ising model. An alternating direction method of multipliers algorithm is used to solve the corresponding convex optimization problems. On synthetic data, we demonstrate that our proposed framework outperforms competitors that do not explicitly model hub nodes. We illustrate our proposal on a webpage data set and a gene expression data set.