Granger causality: Comparative analysis of implementations for Gene Regulatory Networks

Novel algorithms for inferring granger causality using biological data

“…In order to extend the bivariate implementation to the multivariate case, that is, when the 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 > 2, conditional Granger causality is evaluated instead of simple Granger causality [26,30,68,69]. In conditional Granger causality, each variable is left out, in sequence, and its effect on the residual sum of squares is evaluated.…”

“…[52] and Siyal et al [69], consider a scenario of n-variables, where each variable has an equal number of total observational time points 𝑇. This system can be written as a p-order VAR model in the following form:…”

“…In order to evaluate the performance of our proposed method against existing methods, we used two simulated datasets previously used by other researchers to test similar kinds of algorithms [37,69,111,112]. The use of these existing datasets allows us to remain unbiased in our comparison and does not raise questions about the reliability of the datasets.…”

“…The first set of data was used by Mukhopadhyay et al [113]; it simulates a scenario of fourteen variables and uses the following set of mathematical equations: The second set of simulated data was first used by Schelter et al [112] and later in Seth [68], Siyal et al [69], Tam et al [114], and Baccala et al [115]. It simulates a scenario of five variables and uses the following set of equations: As suggested by the above-mentioned authors, we generated the desired quantities of data from these sets of equations by first initializing the equations with white Gaussian noise having zero mean and unit variance.…”

“…In order to determine effectiveness of different variants of Granger causality analysis, we performed a detailed comparative study comparing lasso Granger casualty analysis with other commonly used alternatives, including elastic-net Granger causality, pairwise Granger causality, and standard OLS-based Granger causality [69]. In this study, we compared these four methods using different statistical measures, namely, precision, FDR, F1-Score, and accuracy.…”