Learning Scale Free Networks by Reweighted L1 regularization


Qiang Liu, Alexander Ihler ;
Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR 15:40-48, 2011.


Methods for L1-type regularization have been widely used in Gaussian graphical model selection tasks to encourage sparse structures. However, often we would like to include more structural information than mere sparsity. In this work, we focus on learning so-called “scale-free” models, a common feature that appears in many real-work networks. We replace the L1 regularization with a power law regularization and optimize the objective function by a sequence of iteratively reweighted L1 regularization problems, where the regularization coefficients of nodes with high degree are reduced, encouraging the appearance of hubs with high degree. Our method can be easily adapted to improve any existing L1-based methods, such as graphical lasso, neighborhood selection, and JSRM when the underlying networks are believed to be scale free or have dominating hubs. We demonstrate in simulation that our method significantly outperforms the a baseline L1 method at learning scale-free networks and hub networks, and also illustrate its behavior on gene expression data.

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