Learning an L1-regularized Gaussian Bayesian network in the equivalence class space

Authors:
Diego Vidaurre;Concha Bielza;Pedro Larrañaga
Affiliations:
Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Madrid, Spain;Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Madrid, Spain;Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, Madrid, Spain
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Year:
2010

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Abstract

Learning the structure of a graphical model from data is a common task in a wide range of practical applications. In this paper, we focus on Gaussian Bayesian networks, i.e., on continuous data and directed acyclic graphs with a joint probability density of all variables given by a Gaussian. We propose to work in an equivalence class search space, specifically using the k-greedy equivalence search algorithm. This, combined with regularization techniques to guide the structure search, can learn sparse networks close to the one that generated the data. We provide results on some synthetic networks and on modeling the gene network of the two biological pathways regulating the biosynthesis of isoprenoids for the Arabidopsis thaliana plant.