Fig. 1
Level lines of objective function and penalty terms. Upper panel: Two-dimensional Profile Likelihood for two linearly correlated log-fold-changes, taken from an EPO-induced JAK2/STAT5 signalling pathway [13, 15]. The dashed lines indicate the level lines of an ℓ1 penalty. The gray area marks the 95% confidence region. Lower level: Two-dimensional level lines of constant penalty for the ℓ1/Lasso penalty function and the three extended methods presented in this manuscript: Non-convex ℓq, Adaptive Lasso and Elastic Net penalty. The extended methods can replace the ℓ1 penalty in the upper panel, which is analyzed in the “Results” section. The level lines of ℓ1 are aligned to the gray confidence region, where the extended methods produce a deformation in the level lines that can prevent an alignment