Cross-Validation Estimations of Hyper-Parameters of Gaussian Processes with Inequality Constraints

Abstract : In many situations physical systems may be known to satisfy inequality constraints with respect to some or all input parameters. When building a surrogate model of this system (like in the framework of computer experiments7), one should integrate such expert knowledge inside the emulator structure. We proposed a new methodology to incorporate both equality conditions and inequality constraints into a Gaussian process emulator such that all conditional simulations satisfy the inequality constraints in the whole domain6. An estimator called mode (maximum a posteriori) is calculated and satisfies the inequality constraints. Herein we focus on the estimation of covariance hyper-parameters and cross validation methods1. We prove that these methods are suited to inequality constraints. Applied to real data in two dimensions, the numerical results show that the Leave-One-Out mean square error criterion using the mode is more efficient than the usual (unconstrained) Kriging mean.
Document type :
Conference papers
Complete list of metadatas

https://hal-emse.ccsd.cnrs.fr/emse-01185753
Contributor : Florent Breuil <>
Submitted on : Friday, August 21, 2015 - 2:25:39 PM
Last modification on : Thursday, October 17, 2019 - 12:36:12 PM

Links full text

Identifiers

Citation

Hassan Maatouk, Olivier Roustant, Yann Richet. Cross-Validation Estimations of Hyper-Parameters of Gaussian Processes with Inequality Constraints. Spatial Statistics conference 2015, Jun 2015, Avignon, France. pp.Pages 38-44, ⟨10.1016/j.proenv.2015.07.105⟩. ⟨emse-01185753⟩

Share

Metrics

Record views

307