Error analysis of the kernel regularized regression based on refined convex losses and RKBSs

Abstract

In this paper, we bound the errors of kernel regularized regressions associating with [Formula: see text]-uniformly convex two-sided RKBSs and differentiable [Formula: see text] uniformly smooth losses. In particular, we give learning rates for the learning algorithm with loss [Formula: see text]. Also, we show a probability inequality and with which provide the error bounds for kernel regularized regression with loss [Formula: see text] The discussions are comprehensive applications of the uniformly smooth function theory, the uniformly convex function theory and uniformly convex space theory.