Abstract

Learning network structure underlying data is an important problem in machine learning. This paper presents a novel degree prior to study the inference of scale-free networks, which are widely used to model social and biological networks. In particular, this paper formulates scale-free ne work inference using Gaussian Graphical model (GGM) regularized by a node degree prior. Our degree prior not only promotes a desirable global degree distribution, but also exploits the esti mated degree of an individual node and the relative strength of all the edges of a single node. T fulfill this, this paper proposes a ranking-based method to dynamically estimate the degree of a node, which makes the resultant optimization problem challenging to solve. To deal with this, this paper presents a novel ADMM (alternating direction method of multipliers) procedure. Our experimental results on both synthetic and real data show that our prior not only yields a scalefree network, but also produces many more correctly predicted edges than existing scale-free in ducing prior, hub-inducing prior and the norm.