A finite element method for densityestimation with Gaussian process priors
Date
2010
Authors
Griebel, Michael
Hegland, Markus
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SIAM Publications
Abstract
A variational problem characterizing the density estimator defined by the maximum a posteriori method with Gaussian process priors is derived. It is shown that this problem is well posed and can be solved with Newton's method. Numerically, the solution is approximated by a Galerkin/finite element method with piecewise multilinear functions on uniform grids. Error bounds for this method are given and numerical experiments are performed for one-, two-, and three-dimensional examples.
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Keywords: Error analysis; Finite element method; Galerkin methods; Gaussian distribution; Gaussian noise (electronic); Newton-Raphson method; Density estimation; Density estimator; Gaussian process priors; Maximum a posteriori methods; Multilinear functions; Newton Density estimation; Finite elements; Galerkin; Newton
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SIAM Journal of Numerical Analysis
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Journal article
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2037-12-31
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