Statistics and Data Science Seminar: Theory for Cross Validation in Nonparametric Regression

Abstract: We formulate a general K fold cross validation framework for signal denoising. The general framework is then applied to modern nonlinear 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 nonlinear nonparametric regression methods such as Trend Filtering or Dyadic CART. Our general framework is useful far beyond just the nonparametric regression context and is applicable to a wide range of estimation methods which use tuning parameters, including fundamental methods such as Lasso, Singular value Threshholding etc. 

Bio: Chatterjee is an Assistant Professor (from 2017 onwards) in the Statistics Department at University of Illinois at Urbana Champaign. His research interests include Non Parametric Function Estimation, Statistical Signal Processing, Resampling Methods such as Cross Validation, Statistical Learning Theory and Online Learning Theory. Chatterjee obtained his Phd in 2014 at Yale University and then was a Kruskal Instructor at University of Chicago till 2017.

Host: Soumen Lahiri