Abstract: 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 three solutions --- learning the smoothness using a discrete cosine transform, assuming fatter tails in function-space using a Student-$t$ process, and learning a more flexible kernel using deep kernel learning --- finding some evidence in favor of the first two.