Reproducing Kernel Banach Spaces with the l1 Norm II: Error Analysis for Regularized Least Square Regression

2011/01/24 by Guohui Song, Song, Guohui, Haizhang Zhang +1
Engineering · Mathematics · #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1101.4439

openalex publication_date 2011/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we illustrate how reproducing kernel Banach spaces with the l1 norm can be applied to improve the learning rate estimate of l1-regularization in machine learning.

Citations

• Atomic Decomposition by Basis Pursuit

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