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    Regularized Regression and Density Estimation based on Optimal Transport

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    Type
    Article
    Authors
    Burger, M.
    Franek, M.
    Schonlieb, C.-B.
    KAUST Grant Number
    KUK-I1-007-43
    Date
    2012-03-11
    Permanent link to this record
    http://hdl.handle.net/10754/599489
    
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    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).
    Citation
    Burger M, Franek M, Schonlieb C-B (2012) Regularized Regression and Density Estimation based on Optimal Transport. Applied Mathematics Research eXpress. Available: http://dx.doi.org/10.1093/amrx/abs007.
    Sponsors
    The work of M.B. has been supported by the German Science Foundation (DFG) through project Regularization with Singular Energies. C.B.S acknowledges the financial support provided by the Cambridge Centre for Analysis (CCA), the DFG Graduiertenkolleg 1023 Identification in Mathematical Models: Synergy of Stochastic and Numerical Methods and the project WWTF Five senses-Call 2006, Mathematical Methods for Image Analysis and Processing in the Visual Arts. Further, this publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Oxford University Press (OUP)
    Journal
    Applied Mathematics Research eXpress
    DOI
    10.1093/amrx/abs007
    ae974a485f413a2113503eed53cd6c53
    10.1093/amrx/abs007
    Scopus Count
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