Discrete mixtures of kernels for Kriging-based optimization

Kriging-based exploration strategies often rely on a single Ordinary Kriging model which parametric covariance kernel is selected a priori or on the basis of an initial data set. Since choosing an unadapted kernel can radically harm the results, we wish to reduce the risk of model misspecification. Here we consider the simultaneous use of multiple kernels within Kriging. We give the equations of discrete mixtures of Ordinary Krigings, and derive a multikernel version of the expected improvement optimization criterion. We finally provide an illustration of the Efficient Global Optimization algorithm with mixed exponential and Gaussian kernels, where the parameters are estimated by Maximum Likelihood and the mixing weights are likelihood ratios.