  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 to use statistical
correlations in high-throughput datasets to infer such interactions. However,
cellular pathways are highly cooperative, often requiring the joint effect of
many molecules, and few methods have been proposed to explicitly identify such
higher-order interactions, partially due to the fact that the notion of
multivariate statistical dependency itself remains imprecisely defined. We
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.
