Figure 1

(A) Time-varying topology due to nonlinearities; (B) Prior interpretation and effect of data standardization on the prior distribution. (A) The joint density of the protein pair (x, y) at three different timestamps t1, t2 and t3 caused by a nonlinear response characteristics (upper row). The pair appears uncorrelated at times t1 and t3, but correlated at time t2. Traditional graphical lasso estimates conditional independence relations between them at each time point separately (lower row). Although, the relationship strengths between the protein pair (x, y) at timestamps t1 and t3 are low, the traditional graphical lasso model imposes high penalty to eliminate them. (B) The horizontal and the vertical axes represent variables x and y, respectively. The value of the function f(x,y) = exp(−α|βx − y| − α|βx| − α|y|) is indicated in the colored scale (low - blue; high - red). The quantities α and β denote the regularization and the scaling parameters, respectively. In (I) and (II), we keep the variables x and y in the same scale, i.e, β = 1, and show the impact of different levels of regularization. In (III) and (IV), we choose different scalings for x and y by setting β = 0.5. In figures (I) and (III), we set α = 1 (high regularization). In figures (II) and (IV), we set α = 0.25 (low regularization). The regularization strength impacts equally both variables if the scale parameter β is 1, as seen in figures (I) and (II). However, figures (II) and (IV) show that the impact of the regularization parameter on the variable x is diminished when it is scaled down by lowering β from 1 to 0.5.