Fitting polynomial and spline regression models to measure non-linear relationships. (A-B) A pair of simulated data x,y(black dots) with the black curve illustrating the true expected value E(y) given x, where E(y|x) = cos(x2)2. The red curve shows the fit of a polynomial regression model with degree d = 4 . The blue curve shows the fit of a cubic spline regression model with 2 knots. Fitting indices of the two models are shown at the top. In simulation, polynomial and cubic spline regression models can properly discover non-linear relations. (C-D) Comparisons of regression models and mutual information based co-expression measures in the ND data set. Co-expression of probe pairs is measured with polynomial (d = 3)/cubic spline regressions (x-axis) and mutual information AMI,UniversalVersion 2(y-axis). The Spearman correlation and p-value of the two measures are shown at the top. (E-F) Comparisons in the mouse muscle data set. AMI,UniversalVersion 2has a stronger correlation with regression models than with bicor, indicating that the first two measures can capture certain common non-linear patterns.