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System Parameter Identification by Jose C. Principe, Jinchun Hu, Yu Zhu, Badong Chen

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5

System Identification Under Information Divergence Criteria

The fundamental contribution of information theory is to provide a unified framework for dealing with the notion of information in a precise and technical sense. Information, in a technical sense, can be quantified in a unified manner by using the Kullback–Leibler information divergence (KLID). Two information measures, Shannon’s entropy and mutual information are special cases of KL divergence [43]. The use of probability in system identification is also shown to be equivalent to measuring KL divergence between the actual and model distributions. In parameter estimation, the KL divergence for inference is consistent with common statistical approaches, such as the maximum likelihood ...

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