Functional incremental least square regression algorithm

Abstract

Functional linear regression is one of the main modeling tools for working with functional data. Since functional data are usually stream data essentially and there are some noises in functional data. Many numerical research studies of machine learning indicate that the noise samples not only increase the amount of storage space, but also affect the performance of algorithm. Therefore, in this paper we consider a new learning strategy by introducing incremental learning, Markov sampling for functional linear regression and propose a novel functional incremental linear square regression algorithm based on Markov sampling (FILSR-MS). To have a better understanding of the proposed FILSR-MS, we not only estimate the generalization bound of the proposed algorithm and establish the fast learning rate, but also present some useful discussions. The performance of the proposed algorithm is validated by the numerical experiments for benchmark repository.