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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors present a model for latent functions in regression with which exact inference is possible if the likelihood function is chosen from an exponential family. The latent function is selected with the imposition of a smoothness constraint on a kernel function (of the covariates), which is chosen with information theoretic methods relating proposal distributions. I think the procedure is well motivated with the intention of sacrificing the general flexibility of Gaussian processes for a very favorable complexity of inference. I think the construction of the model and model selection methods are very clean and intuitive.