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An RKHS Approach to Estimation with Gaussian Random Field

  • Author / Creator
    Shuangming Yang
  • One popular approach to estimating an unknown function from noisy data
    is the use of a regularized optimization over a reproducing kernel Hilbert
    space (RKHS). The solution belongs to a nite-dimensional function space.
    If we assume the additive measurement noise is Gaussian, then there is a
    well known statistical interpretation that the RKHS estimate represents the
    posterior mean (minimum variance estimate) of a Gaussian random eld with
    covariance proportional to the kernel associated with the RKHS. In this thesis,
    we calculate the sharp upper bound of the error of the RKHS estimate (given
    unit RKHS norm of the underlying function). We also present a statistical
    interpretation for general loss functions, by assuming the density of prior is
    in exponential form in terms of RKHS norm and then give some simulation
    examples.

  • Subjects / Keywords
  • Graduation date
    Spring 2020
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-0xnw-3r82
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.