  We consider the problem of estimating the parameters of the covariance
function of a Gaussian process by cross-validation. We suggest using new
cross-validation criteria derived from the literature of scoring rules. We also
provide an efficient method for computing the gradient of a cross-validation
criterion. To the best of our knowledge, our method is more efficient than what
has been proposed in the literature so far. It makes it possible to lower the
complexity of jointly evaluating leave-one-out criteria and their gradients.

Computation;Machine Learning