Unveiling complex patterns: An information-theoretic approach to high-order behaviors in microarray data

The information-theoretic approach can shed light on the role of groups of correlated elements within a network. While there are already established methods for measuring new information, storage and transmission, the definition and application of methods for measuring information change remains an unresolved challenge. The change of information in a network is associated with redundancy and synergy between systems that share information about a target. Redundancy involves shared information about the target that can be retrieved using the individual source systems, while synergy involves information that can only be obtained by sharing the systems. A more refined approach, called partial information decomposition (PID), separates the unique, redundant and synergetic contributions of the shared information. However, these contributions cannot be directly derived from the classical measures of information theory. In this work, we apply PID approach to publicly available microarray gene expression data from 2 different experiments derived from patients affected by HCC and ASD. By comparing sample and gene synergy clusters with classical correlation clusters, we uncover higher order behaviours, such as differential genes and enriched functions closely linked to diseases phenotype, that emerge with this novel approach. These findings and further applications of this approach to gene expression data could shed light on the genetic aspects related to physiological aspects of complex diseases.