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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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The radius seven neighbourhood of the class variable in the minimal BIC forest for the breast cancer data. The class variable is shown as a black circle.
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Figure 6: The radius seven neighbourhood of the class variable in the minimal BIC forest for the breast cancer data. The class variable is shown as a black circle.

Mentions: The algorithm took about 18 seconds to find the minimal BIC forest. Figure 6 shows the radius seven neighbourhood of the class variable. The graph suggests that the effect of the p53 mutation on the gene expression profile is mediated by its effect on the expression of a gene with column number 108. This gene is CDC20, a gene involved in cell division. To examine this hypothesis more critically we could apply a richer class of models to this neighbourhood of genes, but that would take us outside the scope of this paper. Figure 6 also shows some apparent hub nodes, including 209 (GPR19), 329 (BUB1), 213 (CENPA), 554 (C10orf3) and 739 (CDCA5), that appear to play a key role in the system. See table 2 of [33] for further information on p53 - associated genes.


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

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

The radius seven neighbourhood of the class variable in the minimal BIC forest for the breast cancer data. The class variable is shown as a black circle.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: The radius seven neighbourhood of the class variable in the minimal BIC forest for the breast cancer data. The class variable is shown as a black circle.
Mentions: The algorithm took about 18 seconds to find the minimal BIC forest. Figure 6 shows the radius seven neighbourhood of the class variable. The graph suggests that the effect of the p53 mutation on the gene expression profile is mediated by its effect on the expression of a gene with column number 108. This gene is CDC20, a gene involved in cell division. To examine this hypothesis more critically we could apply a richer class of models to this neighbourhood of genes, but that would take us outside the scope of this paper. Figure 6 also shows some apparent hub nodes, including 209 (GPR19), 329 (BUB1), 213 (CENPA), 554 (C10orf3) and 739 (CDCA5), that appear to play a key role in the system. See table 2 of [33] for further information on p53 - associated genes.

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