Generalization error bound of semi-supervised learning with ℓ¹ regularization in sum space

This paper proposes a semi-supervised algorithm for least square regularized regression problem with ℓ¹ regularizer in sum space of reproducing kernel Hilbert spaces (RKHSs). By the fact that the sum space has stronger approximation capability than a single hypothesis space and the unlabeled samples can improve the estimation of regression function, an excess error bound for this algorithm can be derived under some assumptions on the kernel, the input space, the marginal distribution, and the regression function. Under some mild conditions, the learning rate of our semi-supervised algorithm can attain l^−Θ with Θ arbitrarily close to 1.