A cross-validation framework for signal denoising with applications to trend filtering, dyadic CART and beyond
本文提出了一个通用的交叉验证框架用于信号去噪，并应用于趋势滤波和二元CART等非参数回归方法，证明其收敛速度与最优调参版本几乎相同，还扩展到了Lasso和奇异值阈值化估计。
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.