A stochastic extended Rippa's algorithm for LpOCV

TL;DR

This paper introduces SERA, a stochastic extension of Rippa's algorithm, which reduces computational costs in kernel-based approximation by efficiently tuning the shape parameter through a novel cross validation approach.

Contribution

The paper presents a new stochastic modification of the extended Rippa's algorithm, improving computational efficiency in shape parameter tuning for kernel approximation.

Findings

SERA significantly reduces computation time.

It maintains high accuracy in shape parameter selection.

Effective across various approximation scenarios.

Abstract

In kernel-based approximation, the tuning of the so-called shape parameter is a fundamental step for achieving an accurate reconstruction. Recently, the popular Rippa's algorithm [14] has been extended to a more general cross validation setting. In this work, we propose a modification of such extension with the aim of further reducing the computational costs. The resulting Stochastic Extended Rippa's Algorithm (SERA) is first detailed and then tested by means of various numerical experiments, which show its efficacy and effectiveness in different approximation settings.