论文标题
剩余交叉验证的集中不平等
Concentration inequalities for leave-one-out cross validation
论文作者
论文摘要
在本文中，我们证明估算器稳定性足以证明通过在一般框架中提供集中界，保留一个输出的交叉验证是一个合理的过程。特别是，我们在Lipschitz的连续性假设上提供了对损耗或估计器的连续性假设。我们通过依靠随机变量的分布来满足对数Sobolev不平等，从而为我们提供了相对丰富的分布类别，从而获得了结果。我们通过考虑几个有趣的示例，包括线性回归，内核密度估计以及稳定/截断的估计器，例如稳定的核回归来说明我们的方法。
In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds in a general framework. In particular, we provide concentration bounds beyond Lipschitz continuity assumptions on the loss or on the estimator. We obtain our results by relying on random variables with distribution satisfying the logarithmic Sobolev inequality, providing us a relatively rich class of distributions. We illustrate our method by considering several interesting examples, including linear regression, kernel density estimation, and stabilized/truncated estimators such as stabilized kernel regression.
