Implications of kernel mismatch for OOD data

Gaussian processes provide reliable uncertainty estimates in nonlinear modeling, but a poor choice of the kernel can lead to slow learning. Although learning the hyperparameters of the kernel typically leads to optimal generalization on in-distribution test data, we show that the generalization can be poor on out-of-distribution test data. We then investigate a smoothness learning method, heavier tails, and deep kernel learning as solutions, finding some evidence in favor of the first two.