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The main idea builds upon the inducing-point formalism underpinning most sparse methods for GP inference. As the computational cost of traditional sparse methods in GPs based on inducing points is O(NM 2), where N is the number of observations and M is the number of inducing points, the paper addresses the problem of large-scale inference by making conditional independence assumptions across inducing points. More specifically, the method proposed in the paper can be seen as a modified version of the partially independent conditional (PIC) approach, where not only the latent functions are grouped in blocks but also the inducing points are clustered in blocks (corresponding to those latent functions) and statistical dependences across inducing point blocks are modeled with a tree. These additional independence assumptions make the resulting inference algorithm much more scalable as it only scales (potentially) linearly with the number of observations and the number of inducing points. The method is evaluated on 1D and 2D problems showing that it outperforms standard sparse GP approximations.