Gaussian process regression with linear inequality constraints

Abstract : The analysis of expensive numerical simulators usually requires metamodelling techniques, among which Gaussian process regression is one of the most popular approaches. Frequently, the code outputs correspond to physical quantities with a behavior which is known a priori: chemical concentrations lie between 0 and 1, the output is increasing with respect to some parameter, etc. In this paper, we introduce a framework for incorporating any type of linear constraints in Gaussian process modeling, including common bound and monotonicity constraints. This new methodology mainly relies on conditional expectations of the truncated multinormal distribution and a discretization of the input space. When dealing with high-dimensional functions, the discretization suffers from the curse of dimensionality. We thus introduce a sequential sampling strategy where the input space is explored via a criterion which maximizes the probability of respecting the given constraints. To further reduce the computational burden, we also recommend a correlation-free approximation. The proposed approaches are evaluated and compared on several analytical functions with different instances of linear constraints.
Type de document :
Pré-publication, Document de travail
2015
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  • HAL Id : hal-01515468, version 1

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Sébastien Da Veiga, Amandine Marrel. Gaussian process regression with linear inequality constraints. 2015. 〈hal-01515468〉

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