一种应用于趋势滤波、Dyadic CART及其他场景的信号去噪交叉验证框架
A Cross Validation Framework for Signal Denoising with Applications to Trend Filtering, Dyadic CART and Beyond
AI总结：
本研究构建了通用的信号去噪交叉验证框架，将其应用于趋势滤波、Dyadic CART等方法，证明其交叉验证版本收敛速率接近最优调参版本，还拓展至高维回归lasso、矩阵估计奇异值阈值法，填补了相关理论空白。
摘要：
本文构建了一个通用的信号去噪交叉验证框架。该通用框架随后被应用于趋势滤波（Trend Filtering）、Dyadic CART等非参数回归方法。研究证明，由此得到的交叉验证版本能够达到与最优调参对应版本近乎一致的收敛速率，而此前尚无针对趋势滤波或Dyadic CART交叉验证版本的理论分析。为阐明该框架的通用性，本文还提出并研究了两种基础估计器的交叉验证版本：适用于高维线性回归的lasso，以及适用于矩阵估计的奇异值阈值法。该通用框架受Chatterjee和Jafarov（2015）的研究思路启发，有望应用于大量使用调优参数的估计方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
