Convergence Rate of Regularized Regression Associated with Zonal Translation Networks

Neural network regularized learning has garnered significant attention in recent years. We give a systematic investigation on the performance of regularized regression associated zonal translation networks. We propose the concept of Marcinkiewicz-Zygmund inequality Setting (MZIS) for the scattered nodes collected from the unit sphere. We show that, under the MZIS, the corresponding convolutional zonal translation network has reproducing property. Based on these facts,we propose a kind of kernel regularized regression learning framework and provide upper bound estimate for the learning rate with the kernel approach. We also give proof for the density of the zonal translation network with spherical Fourier analysis.We provide the approximation error with a K-functional.