2010/03/31 by André Fujita, ANDRÉ FUJITA, JOÃO RICARDO SATO +11
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Autoregressive model #Bioinformatics and Genomic Networks #Biology #Causality (physics) #Computational Drug Discovery Methods #Ecology #Econometrics #Gene Regulatory Network Analysis #Granger causality #Identification (biology) #Mathematics #Multivariate statistics #Statistics
paper · doi:10.1142/s0219720010004860
openalex publication_date 2010/03/31 · crossref created 2010/03/31 · crossref issued 2010/08/01 · crossref published 2010/08/01 · crossref published-print 2010/08/01 · crossref published-online 2011/11/21 · crossref deposited 2021/10/25 · openalex created_date 2025/10/10 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/04
Wiener and Granger have introduced an intuitive concept of causality (Granger causality) between two variables which is based on the idea that an effect never occurs before its cause. Later, Geweke generalized this concept to a multivariate Granger causality, i.e. n variables Granger-cause another variable. Although Granger causality is not "effective causality" in the Aristothelic sense, this concept is useful to infer directionality and information flow in observational data. Granger causality is usually identified by using VAR (Vector Autoregressive) models due to their simplicity. In the last few years, several VAR-based models were presented in order to model gene regulatory networks. Here, we generalize the multivariate Granger causality concept in order to identify Granger causalities between sets of gene expressions, i.e. whether a set of n genes Granger-causes another set of m genes, aiming at identifying the flow of information between gene networks (or pathways). The concept of Granger causality for sets of variables is presented. Moreover, a method for its identification with a bootstrap test is proposed. This method is applied in simulated and also in actual biological gene expression data in order to model regulatory networks. This concept may be useful for the understanding of the complete information flow from one network or pathway to the other, mainly in regulatory networks. Linking this concept to graph theory, sink and source can be generalized to node sets. Moreover, hub and centrality for sets of genes can be defined based on total information flow. Another application is in annotation, when the functionality of a set of genes is unknown, but this set is Granger-caused by another set of genes which is well studied. Therefore, this information may be useful to infer or construct some hypothesis about the unknown set of genes.