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Rebuttal: thank you for your clarifications. I still think that learning kernel (parameters) from multiple realizations of a GP is not very novel in general, but sufficiently novel in your specific context to get discussed at NIPS. The authors use Gaussian processes to learn human function extrapolation behaviour from human sample data. After a comprehensive literature review, they introduce the main idea of the paper: learn the kernel parameters by maximizing the conditional probability of the extrapolation data given the training data. To allow for flexible kernel shapes, they use spectral mixture kernels.