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 genera...

• Type: Journal
• Year: 2010
• Where: BMCBI
• Authors: David Edwards, Gabriel C. G. de Abreu, Rodrigo Labouriau
• Keywords: Algorithms, BMCBI 2010, Gene Expression, Gene Expression Studies