A Cross Validation Framework for Signal Denoising with Applications to Trend Filtering, Dyadic CART and Beyond. (arXiv:2201.02654v2 [math.ST] UPDATED)

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 …

applications arxiv cart framework math signal validation