Statistics Department

Topic:

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.

For more information about Dr. Aditya Guntuboyina, click here.