Coefficient-based [formula omitted]-regularized regression with indefinite kernels and unbounded sampling

Abstract

We consider the kernel-based coefficient least squares learning algorithm for regression with lq-regularizer, 1<q≤2. Our error analysis is carried out under more general conditions. The kernel function may be non-positive definite and the output sample values satisfy the moment hypothesis rather than the uniform boundedness. We derive the capacity dependent error bounds of the algorithm by constructing the stepping stone function for the indefinite kernels. When the output values are bounded, we obtain a learning rate that can be arbitrarily close to the best rate O(m−1) under some mild conditions of the regression function and the hypothesis space.