Abstract

Co-authors : E. Padonou (Mines Saint-Etienne), Y. Deville (AlpeStat), A. Clément (CEA), G. Perrin (CEA), J. Giorla (CEA) and H. Wynn (LSE).

Gaussian processes (GP) are widely used as metamodels for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number of levels (typically several tens), partitioned in groups of various sizes. Parsimonious group covariance functions can then defined by block covariance matrices with constant correlations between pairs of blocks and within blocks.

In this talk, we first present a formulation of GP models with categorical inputs, which makes a synthesis of existing ones and extends the usual homoscedastic and tensor-product frameworks. Then, we give a parameterization of the block covariance matrix described above, based on a hierarchical Gaussian model. The same model can be used when the assumption within blocks is relaxed, giving a flexible parametric family of valid covariance matrices with constant correlations between pairs of blocks.
We illustrate with an application in nuclear engineering, where one of the categorical inputs is the atomic number in Mendeleev's periodic table and has more than 90 levels.