Gaussian processes are the ideal tool for modelling the Galactic ISM, combining statistical flexibility with a good match to the underlying physics. In an earlier paper we outlined how they can be employed to construct three-dimensional maps of dust extinction from stellar surveys. Gaussian processes scale poorly to large datasets though, which put the analysis of realistic catalogues out of reach. Here we show how a novel combination of the Expectation Propagation method and certain sparse matrix approximations can be used to accelerate the dust mapping problem. We demonstrate, using simulated Gaia data, that the resultant algorithm is fast, accurate and precise. Critically, it can be scaled up to map the Gaia catalogue.
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