Vector-valued Reproducing Kernel Banach Spaces with Group Lasso Norms

2019/03/03 by Liangzhi Chen, Chen, Liangzhi, Haizhang Zhang +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1903.00819

openalex publication_date 2019/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Focusing on establishing a mathematical basis for kernel methods in sparse multi-task learning, we explore the theory of vector-valued reproducing kernel Banach spaces (RKBSs) endowed with ℓ_p,1-norms (1≤ p≤ +∞), encompassing both the sparse learning case when p=1 and the group lasso when p=2. We develop RKBSs equipped with these group lasso norms that support the linear representer theorem for regularized learning frameworks. Additionally, we introduce reproducing kernels admissible for this construction. Such reproducing kernels are applicable to sparse multi-task learning with group lasso norms.

Citations

• A Sparse-Group Lasso
• A note on the group lasso and a sparse group lasso
• On Learning Vector-Valued Functions

Related

• Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the ℓ¹ Norm
• Vector-valued Reproducing Kernel Banach Spaces with Applications to Multi-task Learning
• Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
• Consistency of the group Lasso and multiple kernel learning
• Sparse Representer Theorems for Learning in Reproducing Kernel Banach Spaces