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Statistical properties of the method of regularization with periodic Gaussian reproducing kernel
Annals of Statistics
The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization. We show in the white noise model setting, that in function spaces of very smooth functions, such as the infinite-order Sobolev space and the space of analytic functions, the method under consideration is asymptotically minimax; in finite-order Sobolevdoi:10.1214/009053604000000454 fatcat:dcwxyeuqsnb4hehzb5r2rdfcwi