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Application of integral operator for regularized least-square regression

โœ Scribed by Hongwei Sun; Qiang Wu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
583 KB
Volume
49
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

In this paper, we study the consistency of the regularized least-square regression in a general reproducing kernel Hilbert space. We characterize the compactness of the inclusion map from a reproducing kernel Hilbert space to the space of continuous functions and show that the capacity-based analysis by uniform covering numbers may fail in a very general setting. We prove the consistency and compute the learning rate by means of integral operator techniques. To this end, we study the properties of the integral operator. The analysis reveals that the essence of this approach is the isomorphism of the square root operator.

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