Cross-validation is a widely used technique for assessing the performance of
predictive models on unseen data. Many predictive models, such as Kernel-Based
Partial Least-Squares (PLS) models, require the computation of
$\mathbf{X}^{\mathbf{T}}\mathbf{X}$ and $\mathbf{X}^{\mathbf{T}}\mathbf{Y}$
using only training set samples from the input and output matrices,
$\mathbf{X}$ and $\mathbf{Y}$, respectively. In this work, we present three
algorithms that efficiently compute these matrices. The first one allows no
column-wise preprocessing. The second one allows column-wise centering around
the training set means. The third one allows column-wise centering and
column-wise scaling around the training set means and standard deviations.
Demonstrating correctness and superior computational complexity, they offer
significant cross-validation speedup compared with straight-forward
cross-validation and previous work on fast cross-validation - all without data
leakage. Their suitability for parallelization is highlighted with an
open-source Python implementation combining our algorithms with Improved Kernel
PLS.

本文介绍了三种有效计算未见数据集上预测模型性能的算法，它们在计算复杂度和正确性方面表现优越，并且相比于直接交叉验证和快速交叉验证的先前工作，它们提供了显著的交叉验证加速，而无需数据泄漏。同时，本文还重点介绍了这些算法与改进的 Kernel PLS 的开源 Python 实现相结合的并行化功能。

简化交叉验证：高效地导出列向正规化和标准化的训练集 X'X 和 X'Y，避免全量重新计算矩阵乘积或统计矩

Shortcutting Cross-Validation: Efficiently Deriving Column-Wise Centered  and Scaled Training Set $\mathbf{X}^\mathbf{T}\mathbf{X}$ and  $\mathbf{X}^\mathbf{T}\mathbf{Y}$ Without Full Recomputation of Matrix  Products or Statistical Moments