Determining structural identifiability of parameter learning machines

Authors:
Zhi-Yong Ran;Bao-Gang Hu
Affiliations:
-;-
Venue:
Neurocomputing
Year:
2014

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Abstract

This paper reports an extension of our previous study on determining structural identifiability of the generalized 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 the Multiple-input Multiple-output (MIMO) models. This result therefore generalizes the previous one for Single-input Single-output (SISO) and Multiple-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 the Kullback-Leibler divergence (KLD) and regular summary. Third, time-variant models are studied based on the exhaustive summary method. 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.