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2016 Generalization of the Kimeldorf-Wahba correspondence for constrained interpolation
Xavier Bay, Laurence Grammont, Hassan Maatouk
Electron. J. Statist. 10(1): 1580-1595 (2016). DOI: 10.1214/16-EJS1149

Abstract

In this paper, we extend the correspondence between Bayes’ estimation and optimal interpolation in a Reproducing Kernel Hilbert Space (RKHS) to the case of convex constraints such as boundedness, monotonicity or convexity. In the unconstrained interpolation case, the mean of the posterior distribution of a Gaussian Process (GP) given data interpolation is known to be the optimal interpolation function minimizing the norm in the RKHS associated to the GP. In the constrained case, we prove that the Maximum A Posteriori (MAP) or Mode of the posterior distribution is the optimal constrained interpolation function in the RKHS. So, the general correspondence is achieved with the MAP estimator and not the mean of the posterior distribution. A numerical example is given to illustrate this last result.

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Xavier Bay. Laurence Grammont. Hassan Maatouk. "Generalization of the Kimeldorf-Wahba correspondence for constrained interpolation." Electron. J. Statist. 10 (1) 1580 - 1595, 2016. https://doi.org/10.1214/16-EJS1149

Information

Received: 1 February 2016; Published: 2016
First available in Project Euclid: 31 May 2016

zbMATH: 1348.60055
MathSciNet: MR3507374
Digital Object Identifier: 10.1214/16-EJS1149

Subjects:
Primary: 60G15, 60G25, 62K20

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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