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

Edwards D, de Abreu GC, Labouriau R - BMC Bioinformatics (2010)

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Genetics and Biotechnology, Faculty of Agricultural Sciences, Aarhus University, Aarhus, Denmark. David.Edwards@agrsci.dk

ABSTRACT

Background: 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.

Results: 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.

Conclusions: 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.

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A tree and a rooted tree. Specifying a root generates a single-parent DAG.
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Figure 4: A tree and a rooted tree. Specifying a root generates a single-parent DAG.

Mentions: The DAGs that are Markov equivalent to a given tree comprise a Markov equivalence class. As illustrated in Figure 4, they are easily found. Labelling a node (Xr, say) as a root and orienting all edges away from the root, induces a single-parent DAG, that is, one in which all nodes have at most one parent. Any node can be chosen as root. Under such a DAG, the joint distribution factorizes into


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

Edwards D, de Abreu GC, Labouriau R - BMC Bioinformatics (2010)

A tree and a rooted tree. Specifying a root generates a single-parent DAG.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2823705&req=5

Figure 4: A tree and a rooted tree. Specifying a root generates a single-parent DAG.
Mentions: The DAGs that are Markov equivalent to a given tree comprise a Markov equivalence class. As illustrated in Figure 4, they are easily found. Labelling a node (Xr, say) as a root and orienting all edges away from the root, induces a single-parent DAG, that is, one in which all nodes have at most one parent. Any node can be chosen as root. Under such a DAG, the joint distribution factorizes into

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Genetics and Biotechnology, Faculty of Agricultural Sciences, Aarhus University, Aarhus, Denmark. David.Edwards@agrsci.dk

ABSTRACT

Background: 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.

Results: 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.

Conclusions: 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.

Show MeSH
Related in: MedlinePlus