论文标题
信号降级的交叉验证框架，并应用趋势过滤，二元车及其他
A Cross Validation Framework for Signal Denoising with Applications to Trend Filtering, Dyadic CART and Beyond
论文作者
论文摘要
本文制定了一个通用的交叉验证框架，用于信号降解。然后将一般框架应用于非参数回归方法，例如趋势过滤和二元推车。然后显示出所得的交叉验证的版本，以达到与最佳调谐类似物所知的收敛速率几乎相同。没有对趋势过滤或二元推车的交叉验证版本进行的任何理论分析。为了说明框架的普遍性，我们还建议并研究两个基本估计器的交叉验证版本；高维线性回归和奇异值阈值的套索用于矩阵估计。我们的一般框架灵感来自Chatterjee和Jafarov（2015）中的想法，并且可能适用于使用调谐参数的广泛估计方法。
This paper formulates a general cross validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as Trend Filtering and Dyadic CART. The resulting cross validated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross validated versions of Trend Filtering or Dyadic CART. To illustrate the generality of the framework we also propose and study cross validated versions of two fundamental estimators; lasso for high dimensional linear regression and singular value thresholding for matrix estimation. Our general framework is inspired by the ideas in Chatterjee and Jafarov (2015) and is potentially applicable to a wide range of estimation methods which use tuning parameters.
