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

Diego Vidaurre; Concha Bielza; Pedro Larrañaga

doi:10.1109/TSMCB.2009.2036593

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

Diego Vidaurre^*, Concha Bielza, Pedro Larrañaga

^*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

13 Citations (Scopus)

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.

Original language	English
Article number	5382574
Journal	IEEE Transactions on Cybernetics
Volume	40
Issue	5
Pages (from-to)	1231-1242
Number of pages	12
ISSN	1083-4419
DOIs	https://doi.org/10.1109/TSMCB.2009.2036593
Publication status	Published - 1 Oct 2010
Externally published	Yes

Keywords

Equivalence class
gene networks
graphical Gaussian model
k-greedy equivalence search (GES)
Lasso
microarrays
network induction
regularization

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10.1109/TSMCB.2009.2036593

Cite this

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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.",

keywords = "Equivalence class, gene networks, graphical Gaussian model, k-greedy equivalence search (GES), Lasso, microarrays, network induction, regularization",

author = "Diego Vidaurre and Concha Bielza and Pedro Larra{\~n}aga",

year = "2010",

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Learning an L1-regularized Gaussian Bayesian network in the equivalence class space. / Vidaurre, Diego; Bielza, Concha; Larrañaga, Pedro.
In: IEEE Transactions on Cybernetics, Vol. 40, No. 5, 5382574, 01.10.2010, p. 1231-1242.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

TY - JOUR

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AU - Vidaurre, Diego

AU - Bielza, Concha

AU - Larrañaga, Pedro

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AB - 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.

KW - Equivalence class

KW - gene networks

KW - graphical Gaussian model

KW - k-greedy equivalence search (GES)

KW - Lasso

KW - microarrays

KW - network induction

KW - regularization

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

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Keywords

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