A Spectral Analysis of Dot-product Kernels

Understand

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.