Approximation and Estimation Bounds for Subsets of Reproducing Kernel Kreǐn Spaces

Reproducing kernel Kreın spaces are used in learning from data via kernel methods when the kernel is indefinite. In this paper, a characterization of a subset of the unit ball in such spaces is provided. Conditions are given, under which upper bounds on the estimation error and the approximation error can be applied simultaneously to such a subset. Finally, it is shown that the hyperbolic-tangent kernel and other indefinite kernels satisfy such conditions