Conformal Approach To Gaussian Process Surrogate Evaluation With
  Coverage Guarantees
Edgar Jaber Vincent Blot Nicolas Brunel Vincent Chabridon Emmanuel Remy Bertrand Iooss Didier Lucor Mathilde Mougeot Alessandro Leite
Gaussian processes (GPs) are a Bayesian machine learning approach widely used
to construct surrogate models for the uncertainty quantification of computer
simulation codes in industrial applications. It provides both a mean predictor
and an estimate of the posterior prediction variance, the latter being used to
produce Bayesian credibility intervals. Interpreting these intervals relies on
the Gaussianity of the simulation model as well as the well-specification of
the priors which are not always appropriate. We propose to address this issue
with the help of conformal prediction. In the present work, a method for
building adaptive cross-conformal prediction intervals is proposed by weighting
the non-conformity score with the posterior standard deviation of the GP. The
resulting conformal prediction intervals exhibit a level of adaptivity akin to
Bayesian credibility sets and display a significant correlation with the
surrogate model local approximation error, while being free from the underlying
model assumptions and having frequentist coverage guarantees. These estimators
can thus be used for evaluating the quality of a GP surrogate model and can
assist a decision-maker in the choice of the best prior for the specific
application of the GP. The performance of the method is illustrated through a
panel of numerical examples based on various reference databases. Moreover, the
potential applicability of the method is demonstrated in the context of
surrogate modeling of an expensive-to-evaluate simulator of the clogging
phenomenon in steam generators of nuclear reactors.