A Cross Validation Framework for Signal Denoising with Applications to Trend Filtering, Dyadic CART and Beyond
This provides a practical solution for researchers and practitioners in statistics and machine learning needing automated parameter tuning, though it is incremental as it extends existing ideas to new methods.
The paper tackles the problem of selecting tuning parameters for signal denoising methods by formulating a general cross-validation framework, and shows that applying it to methods like Trend Filtering and Dyadic CART achieves nearly optimal convergence rates, with no prior theoretical analysis for these methods.
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.