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Open Access Methodology article

Selecting high-dimensional mixed graphical models using minimal AIC or BIC forests

David Edwards*, Gabriel CG de Abreu and Rodrigo Labouriau

Author Affiliations

Institute of Genetics and Biotechnology, Faculty of Agricultural Sciences, Aarhus University, Aarhus, Denmark

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BMC Bioinformatics 2010, 11:18  doi:10.1186/1471-2105-11-18

Published: 11 January 2010



Chow and Liu showed that the maximum likelihood tree for multivariate discrete distributions may be found using a maximum weight spanning tree algorithm, for example Kruskal's algorithm. The efficiency of the algorithm makes it tractable for high-dimensional problems.


We extend Chow and Liu's approach in two ways: first, to find the forest optimizing a penalized likelihood criterion, for example AIC or BIC, and second, to handle data with both discrete and Gaussian variables. We apply the approach to three datasets: two from gene expression studies and the third from a genetics of gene expression study. The minimal BIC forest supplements a conventional analysis of differential expression by providing a tentative network for the differentially expressed genes. In the genetics of gene expression context the method identifies a network approximating the joint distribution of the DNA markers and the gene expression levels.


The approach is generally useful as a preliminary step towards understanding the overall dependence structure of high-dimensional discrete and/or continuous data. Trees and forests are unrealistically simple models for biological systems, but can provide useful insights. Uses include the following: identification of distinct connected components, which can be analysed separately (dimension reduction); identification of neighbourhoods for more detailed analyses; as initial models for search algorithms with a larger search space, for example decomposable models or Bayesian networks; and identification of interesting features, such as hub nodes.