Group kernels for Gaussian process metamodels with categorical inputs

Abstract : Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G << L groups of various sizes. Parsimonious covariance functions, or kernels, can then be defined by block covariance matrices T with constant covariances between pairs of blocks and within blocks. We study the positive definiteness of such matrices to encourage their practical use. The hierarchical group/level structure, equivalent to a nested Bayesian linear model, provides a parameterization of valid block matrices T. The same model can then be used when the assumption within blocks is relaxed, giving a flexible parametric family of valid covariance matrices with constant covariances between pairs of blocks. The positive definiteness of T is equivalent to the positive definiteness of a smaller matrix of size G, obtained by averaging each block. The model is applied to a problem in nuclear waste analysis, where one of the categorical inputs is atomic number, which has more than 90 levels.
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https://hal.archives-ouvertes.fr/hal-01702607
Contributor : Olivier Roustant <>
Submitted on : Saturday, March 30, 2019 - 3:13:06 PM
Last modification on : Tuesday, April 16, 2019 - 1:28:10 AM

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  • HAL Id : hal-01702607, version 3
  • ARXIV : 1802.02368

Citation

Olivier Roustant, Esperan Padonou, Yves Deville, Aloïs Clément, Guillaume Perrin, et al.. Group kernels for Gaussian process metamodels with categorical inputs. 2019. ⟨hal-01702607v3⟩

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