Regularized Regression and Density Estimation based on Optimal Transport

M. Burger, M. Franek, C.-B. Schonlieb

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29 Scopus citations

Abstract

The aim of this paper is to investigate a novel nonparametric approach for estimating and smoothing density functions as well as probability densities from discrete samples based on a variational regularization method with the Wasserstein metric as a data fidelity. The approach allows a unified treatment of discrete and continuous probability measures and is hence attractive for various tasks. In particular, the variational model for special regularization functionals yields a natural method for estimating densities and for preserving edges in the case of total variation regularization. In order to compute solutions of the variational problems, a regularized optimal transport problem needs to be solved, for which we discuss several formulations and provide a detailed analysis. Moreover, we compute special self-similar solutions for standard regularization functionals and we discuss several computational approaches and results. © 2012 The Author(s).
Original languageEnglish (US)
Pages (from-to)209-253
Number of pages45
JournalApplied Mathematics Research eXpress
Volume2012
Issue number2
DOIs
StatePublished - Mar 11 2012
Externally publishedYes

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