Determining structural identifiability of parameter learning machines
Determining structural identifiability of parameter learning machines
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DOI：
10.1016/j.neucom.2013.08.039
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发表时间：
2014-03
期刊：
影响因子：
6
通讯作者：
Zhi-Yong Ran;Bao-Gang Hu
中科院分区：
文献类型：
--
作者：
Zhi-Yong Ran;Bao-Gang Hu
本文报告了我们先前关于确定广义约束（GC）模型的结构可识别性的研究的扩展，GC模型被认为是参数学习机。可识别性定义了模型参数的唯一性属性。这个属性对于GC模型中那些物理上可解释的参数尤其重要。我们根据模型的类型推导出可识别性标准。首先，通过将模型作为一组从输入空间到输出空间的确定性非线性变换，我们提供了一个检验多输入多输出（MIMO）模型可识别性的标准。因此，该结果推广了先前的单输入单输出（SISO）和多输入单输出（MISO）模型。其次，如果将模型视为随机框架内输入依赖条件分布的均值函数，我们利用kullback - leibler散度（KLD）和规则总结导出了一个可识别准则。第三，基于穷举总结法研究了时变模型。新的可辨识性准则适用于一系列的微分/差分方程模型，只要它们能得到穷举总结。从文献中提出了几个模型例子来检验它们的可识别性。
This paper reports an extension of our previous study on determining structural identifiability of thegeneralized constraint(GC) models, which are considered to be parameter learning machines. Identifiability defines a uniqueness property to the model parameters. This property is particularly important for those physically interpretable parameters in GC models. We derive identifiability criteria according to the types of models. First, by taking the models as a family of deterministic nonlinear transformations from input space to output space, we provide a criterion for examining identifiability of theMultiple-input Multiple-output(MIMO) models. This result therefore generalizes the previous one forSingle-input Single-output(SISO) andMultiple-input Single-output(MISO) models. Second, if considering the models as the mean functions of input-dependent conditional distributions within stochastic framework, we derive an identifiability criterion by means of theKullback–Leibler divergence(KLD) and regular summary. Third, time-variant models are studied based on theexhaustive summarymethod. The new identifiability criterion is valid for a range of differential/difference equation models whenever their exhaustive summaries can be obtained. Several model examples from the literature are presented to examine their identifiability property.