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SUMMARY:Group covariance functions for Gaussian process metamodels with ca
 tegorical inputs - Olivier Roustant (Mines Saint-Étienne )
DTSTART:20180209T090000Z
DTEND:20180209T100000Z
UID:TALK100378@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-authors : E. Padonou (Mines Saint-Etienne)\, Y. Deville (Al
 peStat)\, A. Cl&eacute\;ment (CEA)\, G. Perrin (CEA)\, J. Giorla (CEA) and
  H. Wynn (LSE).  <br><br>Gaussian processes (GP) are widely used as metamo
 dels for emulating time-consuming computer codes. We focus on problems inv
 olving categorical inputs\, with a potentially large number of levels (typ
 ically several tens)\, partitioned in groups of various sizes. Parsimoniou
 s group covariance functions can then defined by block covariance matrices
  with constant correlations between pairs of blocks and within blocks.<br>
 <br>In this talk\, we first present a formulation of GP models with catego
 rical inputs\, which makes a synthesis of existing ones and extends the us
 ual homoscedastic and tensor-product frameworks. Then\, we give a paramete
 rization of the block covariance matrix described above\, based on a hiera
 rchical Gaussian model. The same model can be used when the assumption wit
 hin blocks is relaxed\, giving a flexible parametric family of valid covar
 iance matrices with constant correlations between pairs of blocks. <br>We 
 illustrate with an application in nuclear engineering\, where one of the c
 ategorical inputs is the atomic number in Mendeleev&#39\;s periodic table 
 and has more than 90 levels.<br>
LOCATION:Seminar Room 1\, Newton Institute
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