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

  • Gaussian Random Field
  • Kernel Regression
  • RKHS

• Graduation date

  Spring 2020

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-0xnw-3r82

• License

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