Convex analysis and variational problems
Convex analysis and variational problems
Computing
Regression with the optimised combination technique
ICML '06 Proceedings of the 23rd international conference on Machine learning
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
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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.