Title: Univariate total variation denoising, trend filtering and multivariate Hardy-Krause variation denoising
Authors: Adityanand Guntuboyina - University of California, Berkeley (United States) [presenting]
Abstract: Total variation denoising (TVD) is a popular technique for nonparametric function estimation. We will first present a theoretical optimality result for univariate TVD for estimating piecewise constant functions. We will then present related results for various extensions of univariate TVD including adaptive risk bounds for higher-order TVD (also known as trend filtering) as well as a multivariate extension via the Hardy-Krause Variation which avoids the curse of dimensionality to some extent. We will also mention connections to shape restricted function estimation.