Xavier Bay's Homepage

Ecole des Mines de Saint-Etienne (ENSM-SE), LSTI/Crocus, 3MI
158, cours Fauriel
42 023 Saint-Etienne cedex 2 (FRANCE)
tel: (33) 4.77.42.00.23
e-mail: bay@emse.fr

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Current research papers (2010):

B. Gauthier, X. Bay, Optimal Interpolation in RKHS, Spectral Decomposition of Integral Operators and Application, submitted April 26^th, 2010

Abstract: The orthogonal projection associated to optimal interpolation in a reproducing kernel Hilbert space is characterized by the spectral decomposition of an integral operator. This operator is built from the reproducing kernel and a measure on the interpolation set. As an application, we illustrate how boundary value constraints can be enforced in Gaussian process models.

Keywords: Reproducing kernel Hilbert space, Optimal interpolation, Integral Operator, Kriging, Boundary value constraints

X. Bay, B. Gauthier, Extended Formula For Kriging Interpolation, submitted July 2^nd, 2010

Abstract: In many fields, Kriging interpolation techniques are used within a finite discrete set of known values of a real function (no evaluation or measurement error). In this paper, we extend the simple Kriging formula to the case the function is known on a general (infinite) subset of points. This extension is based on the spectral decomposition of a certain nuclear Hilbert-Schmidt operator. As a step by step application, we revisit the problem of prediction for the Brownian sheet knowing its values on a separation line.

Keywords: Kriging, Gaussian process regression, Gaussian processes, Gaussian measure, regular conditional probability, Gaussian Hilbert spaces, Hilbert-Schmidt operator, reproducing kernel Hilbert space (RKHS), Karhunen-Loève expansion, Brownian sheet, separation line

B. Gauthier, X. Bay, Spectral Decomposition of Integral Operators For Optimal Interpolation in Hilbert Subspaces, submitted November 8^th, 2010

Abstract: The orthogonal projection associated to optimal interpolation in a Hilbert subspace is characterized by the spectral decomposition of

problem adapted integral operators. We then propose a methodology to construct interpolators that take into account an infinite number of information.

As an application, we illustrate how boundary constraints can be enforced in Gaussian process models.

Keywords: Hilbert Subspaces, Optimal interpolation, Integral Operators, Spectral Decomposition, Infinite data set