Bertrand Gauthier

• PhD
• Cardiff University

We describe a natural coisometry from the Hilbert space of all Hilbert-Schmidt operators on a separable reproducing kernel Hilbert space (RKHS)H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-...

We study a relaxed version of the column-sampling problem for the Nyström approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nyström samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surr...

We study a relaxed version of the column-sampling problem for the Nystr\"om approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nystr\"om samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a...

The design of sparse quadratures for the approximation of integral operators related to symmetric positive-semidefinite kernels is addressed. Particular emphasis is placed on the approximation of the main eigenpairs of an initial operator and on the assessment of the approximation accuracy. Special attention is drawn to the design of sparse quadrat...

The construction of optimal designs for random-field interpolation models via convex design theory is considered. The definition of an Integrated Mean-Squared Error (IMSE) criterion yields a particular Karhunen-Loève expansion of the underlying random field. After spectral truncation, the model can be interpreted as a Bayesian (or regularised) line...

We consider experimental design for the prediction of a realization of a second-order random field Z with known covariance function, or kernel, K. When the mean of Z is known, the integrated mean squared error of the best linear predictor, approximated by spectral truncation, coincides with that obtained with a Bayesian linear model. The machinery...

We address the problem of computing integrated mean-squared error (IMSE) optimal designs for interpolation of random fields with known mean and covariance. We assume that the mean squared error is integrated through a discrete measure and restrict the design space to its support. We show that the IMSE and its approximation by spectral truncation ca...

We address the problem of computing integrated mean-squared error (IMSE)-optimal designs for random field interpolation models. A spectral representation of the IMSE criterion is obtained from the eigendecomposition of the integral operator defined by the covariance kernel of the random field and integration measure considered. The IMSE can then be...

We address the problem of computing IMSE (Integrated Mean-Squared Error) optimal designs for random fields interpolation with known mean and covariance. We both consider the IMSE and truncated-IMSE (approximation of the IMSE by spectral truncation). We assume that the MSE is integrated through a discrete measure and restrict the design space to the...

http://afst.cedram.org/afst-bin/fitem?id=AFST_2012_6_21_3_439_0

We propose a spectral approach for the resolution of kernel-based interpolation problems of which numerical solution can not be directly computed. Such a situation occurs in particular when the number of data is infinite. We first consider optimal interpolation in Hilbert subspaces. For a given problem, an integral operator is defined from the unde...