论文标题
点产品内核的光谱分析
A Spectral Analysis of Dot-product Kernels
论文作者
论文摘要
我们提出了与组成点 - 产品核相关的积分运算符的特征值衰减估计值。估计值改进了针对球体上的功率系列内核建立的估计。这使我们能够在相应的繁殖核希尔伯特空间中获得大量的球。我们通过组合点产物内核讨论了统计估计的后果，并突出了近似误差和统计误差之间有趣的权衡，具体取决于组成的数量和内核的平滑度。
We present eigenvalue decay estimates of integral operators associated with compositional dot-product kernels. The estimates improve on previous ones established for power series kernels on spheres. This allows us to obtain the volumes of balls in the corresponding reproducing kernel Hilbert spaces. We discuss the consequences on statistical estimation with compositional dot product kernels and highlight interesting trade-offs between the approximation error and the statistical error depending on the number of compositions and the smoothness of the kernels.
