Pathway Graphical Lasso - Grechkin, Maxim; Fazel, Maryam; Witten, Daniela; Lee, Su-In (Proceedings of the ... AAAI Conference on Artificial Intelligence, 2015)
Graphical models provide a rich framework for summarizing the dependencies among variables. The approach attempts to learn the structure of a Gaussian graphical model (GGM) by maximizing the log likelihood of the data, subject to an penalty on the elements of the inverse co-variance matrix. Most algorithms for solving the graphical lasso problem do not scale to a very large number of variables. Furthermore, the learned network structure is hard to interpret. To overcome these challenges, we propose a novel GGM structure learning method that exploits the fact that for many real-world problems we have prior knowledge that certain edges are unlikely to be present. For example, in gene regulatory networks, a pair of genes that does not participate together in any of the cellular processes, typically referred to as , is less likely to be connected. In computer vision applications in which each variable corresponds to a pixel, each variable is likely to be connected to the nearby variables. In this paper, we propose the , which learns the structure of a GGM subject to pathway-based constraints. In order to solve this problem, we decompose the network into smaller parts, and use a message-passing algorithm in order to communicate among the subnetworks. Our algorithm has orders of magnitude improvement in run time compared to the state-of-the-art optimization methods for the graphical lasso problem that were modified to handle pathway-based constraints.