Multivariate dependence and genetic networks inference.

A critical task in systems biology is the identification of genes that interact to control cellular processes by transcriptional activation of a set of target genes. Many methods have been developed that use statistical correlations in high-throughput data sets to infer such interactions. However, cellular pathways are highly cooperative, often requiring the joint effect of many molecules. Few methods have been proposed to explicitly identify such higher-order interactions, partially due to the fact that the notion of multivariate statistical dependence itself remains imprecisely defined. The authors define the concept of dependence among multiple variables using maximum entropy techniques and introduce computational tests for their identification. Synthetic network results reveal that this procedure uncovers dependencies even in undersampled regimes, when the joint probability distribution cannot be reliably estimated. Analysis of microarray data from human B cells reveals that third-order statistics, but not second-order ones, uncover relationships between genes that interact in a pathway to cooperatively regulate a common set of targets.