On Reproducing Kernel Banach Spaces:Generic Definitions and Unified Framework of Constructions

作     者：Rong Rong LIN Hai Zhang ZHANG Jun ZHANG Rong Rong LIN;Hai Zhang ZHANG;Jun ZHANG

作者机构：School of Mathematics and StatisticsGuangdong University of TechnologyGuangzhou 510520P.R.China School of Mathematics(Zhuhai)and Guangdong Province Key Laboratory of Computational ScienceSun Yat-sen UniversityZhuhai 519082P.R.China Department of Psychology and Department of StatisticsUniversity of MichiganAnn ArborMI48109USA 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第8期

页      面：1459-1483页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Natural Science Foundation of China(Grant Nos.11971490,11901595) Natural Science Foundation of Guangdong Province(Grant No.2018A030313841) Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(Grant No.2020B1212060032) AFOSR(Grant No.FA9550-19-1-0213)through a subcontract from University of California,Los Angeles 

主　　题：Reproducing kernel Banach spaces feature maps reproducing kernels machine learning the representer theorem 

摘      要：Recently,there has been emerging interest in constructing reproducing kernel Banach spaces(RKBS)for applied and theoretical purposes such as machine learning,sampling reconstruction,sparse approximation and functional *** constructions include the reflexive RKBS via a bilinear form,the semi-inner-product RKBS,the RKBS with?~1 norm,the p-norm RKBS via generalized Mercer kernels,*** definitions of RKBS and the associated reproducing kernel in those references are dependent on the ***,relations among those constructions are *** explore a generic definition of RKBS and the reproducing kernel for RKBS that is independent of ***,we propose a framework of constructing RKBSs that leads to new RKBSs based on Orlicz spaces and unifies existing constructions mentioned above via a continuous bilinear form and a pair of feature ***,we develop representer theorems for machine learning in RKBSs constructed in our framework,which also unifies representer theorems in existing RKBSs.