A system and method for identifying high order associations between variables in complex systems that is particularly useful where there is no correlation or weak correlation between variables due to the influence of a third variable, a ternary relationship. The ternary relationship describes how the variation in the pattern of association between a pair of variables, including its sign and strength, is mediated by a third variable. In one embodiment applied to gene expression data, the activity of pairs of correlated genes due to the activity of one or more third genes is shown.