Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression

arXiv:2211.10968v3 Announce Type: replace-cross
Abstract: Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of divide-and-conquer estimators in the scenario that the target function does not necessarily reside in the underlying RKHS. As a decomposition-based scalable approach, the divide-and-conquer estimators of functional linear regression can substantially reduce the algorithmic complexities in time and memory. We develop an …

abstract analysis arxiv convergence cs.lg function functional kernel linear linear regression paper performance regression space statistical stat.ml studies type