Application of integral operator for regularized least-square regression

In this paper, we study the consistency of the regularized least square regression in a general reproducing kernel Hilbert spaces. We characterized the compactness of the inclusion map from a reproducing kernel Hilbert space to the space of continuous functions and showed 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. To this end, we studied the properties of the integral operator. The analysis reveals that the essence of this approach is the isomorphism of the square root operator. ∗Corresponding author