Application of integral operator for regularized least-square regression

Authors:
Hongwei Sun;Qiang Wu
Affiliations:
School of Science, Jinan University, Jinan 250022, PR China;Department of Statistic Science, Institute for Genome Sciences & Policy, Duke University, Durham, NC 27708, USA
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 7
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Abstract

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.