First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes a variational bound on the length scale parameters of square-exponential-kernel Gaussian process regression models. The main idea is to separate the function to be inferred into a standardised sample from a unit-length-scale square-exponential kernel, and a linear scaling map of that latent function, then to impose factorisation between these two objects via a variational bound. The paper is well written. It uses clear language and provides a compact introduction to previous work.

We introduce a novel variational method that allows to approximately integrate out kernel hyperparameters, such as length-scales, in Gaussian process regression. This approach consists of a novel variant of the variational framework that has been recently developed for the Gaussian process latent variable model which additionally makes use of a standardised representation of the Gaussian process. We consider this technique for learning Mahalanobis distance metrics in a Gaussian process regression setting and provide experimental evaluations and comparisons with existing methods by considering datasets with high-dimensional inputs.

We introduce a novel variational method that allows to approximately integrate out kernel hyperparameters, such as length-scales, in Gaussian process regression. This approach consists of a novel variant of the variational framework that has been recently developed for the Gaussian process latent variable model which additionally makes use of a standardised representation of the Gaussian process. We consider this technique for learning Mahalanobis distance metrics in a Gaussian process regression setting and provide experimental evaluations and comparisons with existing methods by considering datasets with high-dimensional inputs.