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

TL;DR

This paper explores how reproducing kernel Banach spaces with the l1 norm can enhance the error analysis in regularized least squares regression, leading to improved learning rate estimates in machine learning.

Contribution

It demonstrates the application of reproducing kernel Banach spaces with the l1 norm to refine error bounds in l1-regularized learning schemes.

Findings

Improved learning rate estimates for l1-regularization.

Application of reproducing kernel Banach spaces to error analysis.

Reduction of hypothesis error in regularized learning.

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.