Vector-valued Reproducing Kernel Banach Spaces with Applications to Multi-task Learning

2011/11/04 by Haizhang Zhang, Jun Zhang, Zhang, Haizhang +1 · 2 citations
Computer Science · Engineering · #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (stat.ML) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1111.1037

openalex publication_date 2011/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RKBS. The theory is then applied to multi-task machine learning. Especially, the representer theorem and characterization equations for the minimizer of regularized learning schemes in vector-valued RKBS are established.

Cited by

• Adaptive Vector-Valued Splines for the Resolution of Inverse Problems
• Relative reproducing kernels in vector-valued Hilbert and Banach spaces

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