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The automation of posterior inference in Bayesian data analysis has enabledexperts and nonexperts alike to use more sophisticated models, engage in fasterexploratory modeling and analysis, and ensure experimental reproducibility.However, standard automated posterior inference algorithms are not tractable atthe scale of massive modern datasets, and modifications to make them so aretypically model-specific, require expert tuning, and can break theoreticalguarantees on inferential quality. Building on the Bayesian coresets framework,this work instead takes advantage of data redundancy to shrink the datasetitself as a preprocessing step, providing fully-automated, scalable Bayesianinference with theoretical guarantees. We begin with an intuitive reformulationof Bayesian coreset construction as sparse vector sum approximation, anddemonstrate that its automation and performance-based shortcomings arise fromthe use of the supremum norm. To address these shortcomings we develop Hilbertcoresets, i.e., Bayesian coresets constructed under a norm induced by aninner-product on the log-likelihood function space. We propose two Hilbertcoreset construction algorithms---one based on importance sampling, and onebased on the Frank-Wolfe algorithm---along with theoretical guarantees onapproximation quality as a function of coreset size. Since the exactcomputation of the proposed inner-products is model-specific, we automate theconstruction with a random finite-dimensional projection of the log-likelihoodfunctions. The resulting automated coreset construction algorithm is simple toimplement, and experiments on a variety of models with real and syntheticdatasets show that it provides high-quality posterior approximations and asignificant reduction in the computational cost of inference.

Automated Scalable Bayesian Inference via Hilbert Coresets