Fig. 2

Sketch of sensitivity correlation measure. a, b The sensitivity correlation (S) is the difference between the Pearson correlation (\({\rho }_{XY}\)) and the partial correlation (\({\rho }_{XY|Z}\)). Two extreme situations are reported: a the correlation is direct and the miRNA is not mediating the interaction; b the correlation is undirected and the miRNA is mediating the interaction. In the first case, \({\rho }_{XY|Z}= {\rho }_{XY}\), S = 0, and, since Z is not explaining anything, the residuals are highly correlated. In the second case \({\rho }_{XY|Z}=0\), S is maximum, and, since Z is explaining all the variability, no correlation is found between residuals. (c) Heatmap of S, calculated for the top-correlated RNA pairs (i.e., showing \({\rho }_{XY}\) > 0.7) in the normal breast dataset [13]. Bright vertical stripes refer to a small set of miRNAs mediating the interactions between the top-correlated RNA pairs; S values increases from red (S = 0) to blue (S = 1)