title: Learning an L1-regularized Gaussian Bayesian network in the equivalence class space.
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.
authors.affiliation: Departamento de Inteligencia Artificial, Universidad Politécnica de Madrid, 28660 Madrid, Spain.
authors.forename: Diego
authors.initials: D
authors.lastname: Vidaurre
authors.forename: Concha
authors.initials: C
authors.lastname: Bielza
authors.forename: Pedro
authors.initials: P
authors.lastname: Larrañaga
mesh_terms: D000465:Algorithms; D017360:Arabidopsis / Q000378:metabolism*; D001499:Bayes Theorem; D003198:Computer Simulation; D005786:Gene Expression Regulation / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D016011:Normal Distribution; D010940:Plant Proteins / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*; D013729:Terpenes / Q000378:metabolism*
chemical_list: D010940:Plant Proteins; D013729:Terpenes