Table 1.
Examples of applicability of regularization methods for different parameter subgroup structures.
Fig 1.
(A) Plots of the regularization function for the standard LASSO approach, i.e., penalization of logarithmized fold-change parameter values different from zero, and penalization landscapes for the two-dimensional case. (B) Regularization function for the symmetric penalization of fold-change differences via the clustered LASSO, evaluated each for the L1 and L0.8 penalizations.
Fig 2.
(A) Schematic representation of the model structure. Each arrow represents a degradation reaction in one of the three cell types. (B) Model parameter values used for simulation, i.e., the kinetic rate constants and initial concentrations used in the three cell types. (C) A typical data realization (means and error bars) with un-regularized model fits (lines). (D) Objective function landscapes with the regularized best-fit parameter vector (red dot) for different regularization strengths λ. Square brackets indicate a significant decrease in likelihood in terms of a likelihood ratio test.
Fig 3.
(A) A schematic representation of the structure of the model used in [27]. (B) A typical data realization (dots) with model fits before regularization (lines and shaded areas). (C) Parameter values used for simulation of the data for the five cell types. (D) Schematic representation of the simulation study work-flow. (E) The number of times each individual fold-change parameter and difference of fold-change parameters is constrained to zero in the parsimonious model is plotted as a histogram for the standard LASSO approach (blue) and the symmetric penalization of fold-change differences (red). A gray bin background indicates the true values that were used for simulation of the data.
Fig 4.
Comparison of receptor surface level values from [28]. for EGF, ErbB2, ErbB3, IGF-1 and Met receptors for the different cell-lines H322M, BxPc3, A431, BT-20, ACHN, ADRr and IGROV-1 with the estimated initial values from the mathematical model, as well as the results from regularization with symmetric penalization of fold-change differences.