Learning Scale-Free Networks by Dynamic Node-Specific Degree Prior
This work addresses the challenge of accurately inferring scale-free networks, which are crucial for modeling social and biological systems, by proposing a novel prior that improves edge prediction accuracy over previous approaches.
The paper tackles the problem of learning scale-free network structures by introducing a dynamic node-specific degree prior that incorporates ranking and considers both global degree distribution and individual node edge strengths. Experiments on synthetic and real data show that this prior yields scale-free networks and produces significantly more correctly predicted edges compared to existing methods like the scale-free inducing prior, hub-inducing prior, and l1 norm.
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks. The prior not only favors a desirable global node degree distribution, but also takes into consideration the relative strength of all the possible edges adjacent to the same node and the estimated degree of each individual node. To fulfill this, ranking is incorporated into the prior, which makes the problem challenging to solve. We employ an ADMM (alternating direction method of multipliers) framework to solve the Gaussian Graphical model regularized by this prior. Our experiments on both synthetic and real data show that our prior not only yields a scale-free network, but also produces many more correctly predicted edges than the others such as the scale-free inducing prior, the hub-inducing prior and the $l_1$ norm.