Zimmer Christoph, Sahle Sven
BIOMS, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany.
BioQuant/COS Heidelberg, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany.
Biosystems. 2015 Nov;137:55-63. doi: 10.1016/j.biosystems.2015.08.003. Epub 2015 Sep 8.
Parameter estimation procedures are a central aspect of modeling approaches in systems biology. They are often computationally expensive, especially when the models take stochasticity into account. Typically parameter estimation involves the iterative optimization of an objective function that describes how well the model fits some measured data with a certain set of parameter values. In order to limit the computational expenses it is therefore important to apply an adequate stopping criterion for the optimization process, so that the optimization continues at least until a reasonable fit is obtained, but not much longer. In the case of stochastic modeling, at least some parameter estimation schemes involve an objective function that is itself a random variable. This means that plain convergence tests are not a priori suitable as stopping criteria. This article suggests a termination criterion suited to optimization problems in parameter estimation arising from stochastic models in systems biology. The termination criterion is developed for optimization algorithms that involve populations of parameter sets, such as particle swarm or evolutionary algorithms. It is based on comparing the variance of the objective function over the whole population of parameter sets with the variance of repeated evaluations of the objective function at the best parameter set. The performance is demonstrated for several different algorithms. To test the termination criterion we choose polynomial test functions as well as systems biology models such as an Immigration-Death model and a bistable genetic toggle switch. The genetic toggle switch is an especially challenging test case as it shows a stochastic switching between two steady states which is qualitatively different from the model behavior in a deterministic model.
参数估计程序是系统生物学建模方法的核心内容。它们通常计算成本高昂，尤其是当模型考虑到随机性时。通常，参数估计涉及对目标函数进行迭代优化，该目标函数描述了模型在某组参数值下与某些测量数据的拟合程度。因此，为了限制计算成本，为优化过程应用适当的停止准则很重要，这样优化至少持续到获得合理的拟合，但不会持续更长时间。在随机建模的情况下，至少一些参数估计方案涉及一个本身就是随机变量的目标函数。这意味着普通的收敛测试并非天生适合作为停止准则。本文提出了一种适用于系统生物学中随机模型参数估计优化问题的终止准则。该终止准则是为涉及参数集群体的优化算法开发的，例如粒子群算法或进化算法。它基于比较整个参数集群体上目标函数的方差与在最佳参数集处对目标函数进行重复评估的方差。展示了几种不同算法的性能。为了测试终止准则，我们选择了多项式测试函数以及系统生物学模型，如迁入 - 死亡模型和双稳态基因开关。基因开关是一个特别具有挑战性的测试案例，因为它显示了在两个稳态之间的随机切换，这与确定性模型中的模型行为在定性上有所不同。
