Solving $\ell^p\!$-norm regularization with tensor kernels

TL;DR

This paper introduces a fast dual algorithm utilizing tensor kernels to efficiently solve nonparametric $ ext{ell}^p$-norm regularized learning problems, challenging the belief that kernel methods are limited to Hilbert spaces.

Contribution

It proposes a novel dual algorithm with tensor kernels for $ ext{ell}^p$ regularization, extending kernel methods beyond Hilbert spaces.

Findings

The algorithm is computationally efficient.

Numerical experiments demonstrate effectiveness.

Challenges previous limitations of kernel methods.

Abstract

In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of $\ell^p$ regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast recent findings suggesting kernel methods cannot be extended beyond Hilbert setting. Numerical experiments confirm the effectiveness of the method.