Regularized regression and density estimation based on optimal transport

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Burger M, Franek M, Schönlieb CB
Zeitschrift: Applied Mathematics Research eXpress
Jahr der Veröffentlichung: 2012
Band: 2012
Seitenbereich: 209-253
ISSN: 1687-1200
eISSN: 1687-1197
Sprache: Englisch


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).


Einrichtungen weiterer Autorinnen und Autoren

University of Cambridge
Westfälische Wilhelms-Universität (WWU) Münster


Zitierweisen

APA:
Burger, M., Franek, M., & Schönlieb, C.B. (2012). Regularized regression and density estimation based on optimal transport. Applied Mathematics Research eXpress, 2012, 209-253. https://dx.doi.org/10.1093/amrx/abs007

MLA:
Burger, Martin, Marzena Franek, and Carola Bibiane Schönlieb. "Regularized regression and density estimation based on optimal transport." Applied Mathematics Research eXpress 2012 (2012): 209-253.

BibTeX: 

Zuletzt aktualisiert 2019-23-08 um 21:50