Univariate total variation denoising, trend filtering and multivariate Hardy-Krause variation denoising

Abstract:
Total variation denoising (TVD) is a popular technique for nonparametric function estimation. I will first present a theoretical optimality result for univariate TVD for estimating piecewise constant functions. I 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. I will also mention connections to shape restricted function estimation. The results are based on joint work with Sabyasachi Chatterjee, Billy Fang, Donovan Lieu and Bodhisattva Sen.

Biography:
Aditya Guntuboyina is currently an Associate Professor at the Department of Statistics, UC Berkeley. He has been at Berkeley since 2012 after finishing his PhD in Statistics from Yale University and a postdoctoral position at the Wharton Statistics Department in the University of Pennsylvania. His research interests include nonparametric and high-dimensional statistics, shape constrained statistical estimation, empirical processes and statistical information theory. His research is currently supported by an NSF CAREER award.

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