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A Learning‐Theoretic Approach To Model‐Set Identification
Authors:Yasuaki Oishi  Hidenori Kimura
Abstract:A new approach to model‐set identification is proposed based on an agnostic learning theory. The squared prediction error is estimated together with its uncertainty uniformly in some parameter region. Based on this estimation, a model set is constructed so as to include the best model. The proposed approach does not require assumptions on the true dynamics or the noise, neither does it need infinite number of input‐output data in order to justify its result. But it guarantees that the size of the identified model set converges to zero as the number of input‐output data increases. Improvement of the precision is considered on the proposed identification method. Generalization of the approach is discussed and a numerical example is presented.
Keywords:Model‐set identification  agnostic learning theory  law of large numbers  sample complexity  robust control
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