Finetuning greedy kernel models by exchange algorithms

TL;DR

This paper introduces kernel exchange algorithms (KEA) that combine knot insertion and removal to refine greedy kernel surrogate models, significantly reducing approximation errors without increasing computational costs.

Contribution

The paper presents a novel class of kernel exchange algorithms that enhance kernel interpolation accuracy by combining knot insertion and removal strategies.

Findings

Error reduction up to 86.4% in experiments

Average error reduction of 17.2%

Improved kernel model accuracy without added computational complexity

Abstract

Kernel based approximation offers versatile tools for high-dimensional approximation, which can especially be leveraged for surrogate modeling. For this purpose, both "knot insertion" and "knot removal" approaches aim at choosing a suitable subset of the data, in order to obtain a sparse but nevertheless accurate kernel model. In the present work, focussing on kernel based interpolation, we aim at combining these two approaches to further improve the accuracy of kernel models, without increasing the computational complexity of the final kernel model. For this, we introduce a class of kernel exchange algorithms (KEA). The resulting KEA algorithm can be used for finetuning greedy kernel surrogate models, allowing for an reduction of the error up to 86.4% (17.2% on average) in our experiments.