Performance of objective functions and optimization procedures for parameter estimation in system biology models
Andrea Degasperi, Dirk Fey & Boris N. Kholodenko, Performance of objective functions and optimisation procedures for parameter estimation in system biology models, 2017, Systems Biology and Applications volume 3, Article number: 20
In systems biology, relative data are a common occurrence. In ODE-based models, this is regarded by either introducing scaling parameters or data-driven normalization to bring data and simulations onto the same scale. It was shown in this article, that data-driven normalization improves optimization performance and does not aggravate non-identifiability problems compared to a scaling factor approach. Furthermore, this article reports that hybrid optimization methods which combine stochastic global and deterministic local search outperforms deterministic local gradient-based strategies.
3 Study outcomes
Employing data-driven normalization instead of scaling factors improved the identifiability of dynamic parameters, providing a computational example to demonstrate how this occurs.
3.2 Convergence Speed
As visualized in Fig. 4 and Fig. 5 of the original publication, convergence speed was consistently improved using data driven normalization compared to scaling factors. Combining the data-driven normalization with the hybrid optimization algorithm GLSDC provided the best performance results especially in high-parameter settings.
4 Study design and evidence level
- The provided claims are tested on 3 parameter estimation problems with varying amount of parameters.
- The 3 main algorithms tested were GLSDC, LevMar SE, LevMar FD with scaling factors and data normalization each. These were tested in 96 runs each.
- Although the previously best-performing method using LSQNONLIN with sensitivity equations as found in Lessons Learned from Quantitative Dynamical Modeling in Systems Biology has been mentioned, but a comparison with GLSDC was restricted to use of their implementation of the algorithm.
- The study used Least-Squares instead of Likelihood as objective function, omitting error model fits.
5 Further comments and aspects
- Additionally to the performance advantages of not using scaling factors, it is also stated that the amount of overfitting is reduced.
- The notion of practical identifiability does deviates from other literature, see for example e.g. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood
- The objective function values in Fig. 4 and Fig. 5 are not entirely obvious to interpret, since stochastic algorithms and multi-start algorithms are analyzed.