Uniform Random Generation of Large Acyclic Digraphs

Kuipers, Jack and Moffa, Giusi. (2015) Uniform Random Generation of Large Acyclic Digraphs. Statistics and Computing, 25. pp. 227-242.

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Official URL: https://edoc.unibas.ch/81030/

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Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Statistik (Moffa)
UniBasel Contributors:Moffa, Giusi
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:13 Apr 2021 13:43
Deposited On:13 Apr 2021 13:43

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