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.

本文研究了使用具有各向异性高斯 RBF 核的 SVM 的非参数回归问题。在目标函数驻留在某些各向异性 Besov 空间中的假设下，我们建立了几乎最佳的学习率，更准确地说，最佳的达到某个对数因子，由有效平滑度表示。通过考虑有效平滑度，我们几乎最优的学习率比使用特定各向异性 Sobolev 空间的基础 RKHS 获得的学习率更快。此外，如果目标函数仅依赖于较少的维度，则可以进一步实现更快的学习率。