SIAM Journal on Matrix Analysis and Applications, Volume 42, Issue 3, Page 1073-1095, January 2021.
This paper presents a preconditioner-based method for solving a kernel ridge regression problem. In contrast to other methods, which utilize either fast matrix-vector multiplication or a preconditioner, the suggested approach uses randomized matrix decompositions for building a preconditioner with a special structure that can also utilize fast matrix-vector multiplications. This hybrid approach is efficient in reducing the condition number, exact, and computationally efficient, enabling the processing of large datasets with computational complexity linear to the number of data points. Also, a theoretical upper bound for the condition number is provided. For Gaussian kernels, we show that given a desired condition number, the rank of the needed preconditioner can be determined directly from the dataset.

中文翻译：

---

使用矩阵分解进行预处理的快速准确的高斯核岭回归

SIAM 矩阵分析与应用杂志，第 42 卷，第 3 期，第 1073-1095 页，2021 年 1 月。
本文提出了一种基于预处理器的方法来解决核岭回归问题。与使用快速矩阵向量乘法或预处理器的其他方法相比，建议的方法使用随机矩阵分解来构建具有特殊结构的预处理器，该结构也可以利用快速矩阵向量乘法。这种混合方法可以有效地减少条件数，准确且计算效率高，能够处理计算复杂度与数据点数量成线性关系的大型数据集。此外，还提供了条件数的理论上限。对于高斯核，我们表明，给定所需的条件数，可以直接从数据集中确定所需预处理器的等级。