Selecting high-dimensional mixed graphical models using minimal AIC or BIC forests.
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.
Edwards
David
D
Institute of Genetics and Biotechnology, Faculty of Agricultural Sciences, Aarhus University, Aarhus, Denmark. David.Edwards@agrsci.dk
de Abreu
Gabriel C G
GC
Labouriau
Rodrigo
R
D000465:Algorithms; D001943:Breast Neoplasms / Q000235:genetics; D005260:Female; D020869:Gene Expression Profiling / Q000379:methods; D053263:Gene Regulatory Networks; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D010363:Pattern Recognition, Automated