论文标题
降低维度的核心稳定性
Dimensionality Reduction and Wasserstein Stability for Kernel Regression
论文作者
论文摘要
在高维回归框架中，我们研究了幼稚的两步程序的后果，其中首先减少了输入变量的维度，其次是使用减少的输入变量来预测核回归的输出变量。为了分析所得的回归误差，得出了核回归的新稳定性结果。这使我们能够限制使用扰动输入数据以适合回归函数时发生的错误。我们将一般稳定性结果应用于主成分分析（PCA）。利用有关主成分分析和内核回归的文献中的已知估计值，我们推断了两步程序的收敛速率。后者在半监督环境中特别有用。
In a high-dimensional regression framework, we study consequences of the naive two-step procedure where first the dimension of the input variables is reduced and second, the reduced input variables are used to predict the output variable with kernel regression. In order to analyze the resulting regression errors, a novel stability result for kernel regression with respect to the Wasserstein distance is derived. This allows us to bound errors that occur when perturbed input data is used to fit the regression function. We apply the general stability result to principal component analysis (PCA). Exploiting known estimates from the literature on both principal component analysis and kernel regression, we deduce convergence rates for the two-step procedure. The latter turns out to be particularly useful in a semi-supervised setting.
