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

In this paper, we bound the errors of kernel regularized regressions associating with 2 -uniformly convex two-sided RKBSs and differentiable σ (t) = | t | p p (1 < p ≤ 2) uniformly smooth losses. In particular, we give learning rates for the learning algorithm with loss V p (t) = | t | p p (1 < p ≤ 2). Also, we show a probability inequality and with which provide the error bounds for kernel regularized regression with loss V q (t) = | t | q q (q > 2). The discussions are comprehensive applications of the uniformly smooth function theory, the uniformly convex function theory and uniformly convex space theory. [ABSTRACT FROM AUTHOR]