SPEAKER: Aditya Guntuboyina, Associate Professor of Statistics, UC Berkeley
TITLE: "Multivariate extensions of isotonic regression and total variation denoising via entire monotonicity and Hardy-Krause variation"
ABSTRACT: Isotonic regression and total variation denoising are two widely used univariate nonparametric function estimation methods that fit piecewise constant functions to data. I will describe natural extensions of these to the multivariate setting. Typical multivariate nonparametric estimation methods suffer from the curse of dimensionality. In contrast, our extensions avoid the dimensionality curse to a reasonable extent. These techniques can be used to fit rectangular piecewise constant functions to data via convex optimization. This is joint work with Billy Fang and Bodhisattva Sen.