Correspondance entre régression par processus Gaussien et splines d'interpolation sous contraintes linéaires de type inégalité. Théorie et applications.

Abstract : This thesis is dedicated to interpolation problems when the numerical function is known to satisfy some properties such as positivity, monotonicity or convexity. Two methods of interpolation are studied. The first one is deterministic and is based on convex optimization in a Reproducing Kernel Hilbert Space (RKHS). The second one is a Bayesian approach based on Gaussian Process Regression (GPR) or Kriging. By using a finite linear functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that conditional simulations satisfy all the inequality constraints. As a consequence, GPR is equivalent to the simulation of a truncated Gaussian vector to a convex set. The mode or Maximum A Posteriori is defined as a Bayesian estimator and prediction intervals are quantified by simulation. Convergence of the method is proved and the correspondence between the two methods is done. This can be seen as an extension of the correspondence established by [Kimeldorf and Wahba, 1971] between Bayesian estimation on stochastic process and smoothing by splines. Finally, a real application in insurance and finance is given to estimate a term-structure curve and default probabilities.
Document type :
Theses
Complete list of metadatas

Cited literature [88 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01282224
Contributor : Abes Star <>
Submitted on : Thursday, March 3, 2016 - 2:22:16 PM
Last modification on : Tuesday, October 23, 2018 - 2:36:09 PM
Long-term archiving on : Saturday, June 4, 2016 - 11:03:01 AM

File

Matouk-hassan-diff.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01282224, version 1

Citation

Hassan Maatouk. Correspondance entre régression par processus Gaussien et splines d'interpolation sous contraintes linéaires de type inégalité. Théorie et applications.. Autre. Ecole Nationale Supérieure des Mines de Saint-Etienne, 2015. Français. ⟨NNT : 2015EMSE0791⟩. ⟨tel-01282224⟩

Share

Metrics

Record views

1119

Files downloads

1221