  This paper investigates the nonparametric regression problem using SVMs with
anisotropic Gaussian RBF kernels. Under the assumption that the target
functions are resided in certain anisotropic Besov spaces, we establish the
almost optimal learning rates, more precisely, optimal up to some logarithmic
factor, presented by the effective smoothness. By taking the effective
smoothness into consideration, our almost optimal learning rates are faster
than those obtained with the underlying RKHSs being certain anisotropic Sobolev
spaces. Moreover, if the target function depends only on fewer dimensions,
faster learning rates can be further achieved.
