A finite element method for densityestimation with Gaussian process priors

Date

2010

Authors

Griebel, Michael
Hegland, Markus

Journal Title

Journal ISSN

Volume Title

Publisher

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.

Description

Keywords

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

Citation

Source

SIAM Journal of Numerical Analysis

Type

Journal article

Book Title

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Restricted until

2037-12-31