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Learning the network structure underlying data is an important problem inmachine learning. This paper introduces a novel prior to study the inference ofscale-free networks, which are widely used to model social and biologicalnetworks. The prior not only favors a desirable global node degreedistribution, but also takes into consideration the relative strength of allthe possible edges adjacent to the same node and the estimated degree of eachindividual node.  To fulfill this, ranking is incorporated into the prior, which makes theproblem challenging to solve. We employ an ADMM (alternating direction methodof multipliers) framework to solve the Gaussian Graphical model regularized bythis prior. Our experiments on both synthetic and real data show that our priornot only yields a scale-free network, but also produces many more correctlypredicted edges than the others such as the scale-free inducing prior, thehub-inducing prior and the $l_1$ norm.

Learning Scale-Free Networks by Dynamic Node-Specific Degree Prior