Regularized regression and density estimation based on optimal transport

Burger M, Franek M, Schönlieb CB (2012)

Publication Language: English

Publication Type: Journal article

Publication year: 2012

Journal

Applied Mathematics Research eXpress Oxford University Press

Book Volume: 2012

Pages Range: 209-253

Issue: 2

DOI: 10.1093/amrx/abs007

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).

Authors with CRIS profile

Martin Burger

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) University of Cambridge GB United Kingdom (GB)

How to cite

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.

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