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The paper marries a sparse approximation to the black-box inference method of [6], and demonstrates its effectiveness on a pleasingly wide variety of problems. I almost can't believe it took us this long for this paper to be written, but I'm happy that it has. It made sense once I realized it was referring to [6], but I wonder if there isn't a better word than "automated" to describe the fact that it can handle black-box likelihood functions. Quality and clarity: The intro was fairly clearly written, although I don't understand why the term "statistical efficiency" is used to describe a bound being well-approximated. Shouldn't statistical efficiency refer to taking full advantage of the available data? How can the computational complexity ( O(M 3)) not depend on the number of datapoints?