Xavier Bay's Homepage
Current research papers (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
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
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