Finetuning greedy kernel models by exchange algorithms
This work addresses the need for more accurate and efficient kernel models in high-dimensional approximation, though it appears incremental as it builds on existing greedy methods.
The paper tackles the problem of improving the accuracy of kernel-based surrogate models without increasing computational complexity by combining knot insertion and removal approaches, resulting in an error reduction of up to 86.4% (17.2% on average) in experiments.
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.