Quantitative Indexes of System Identifiability: An Approach Based on Consistent Measures of Dependence

The paper is concerned with the problem of quantitative characterizing the identifiability of systems. Such a characterization is based on applying dependence properties of two random values, one of which represents a component of the system input variable, the second one represents a component of the system output variable. In turn, the dependence properties are described by a measure of stochastic dependence. A measure of heterogeneity of the impact of input variables of a system into the output one, based on measures of dependence meeting the Rényi's axioms, is proposed. Applying the Cauchy-Schwarz divergence, an information theoretic measure of dependence meeting “almost all” Rényi's axioms is also proposed. The paper has been supported by a grant of the Russian Foundation for Basic Researches (RFBR): project 12-08-01205-a.