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SUMMARY This paper presents an idea that would be very interesting to NIPS readers. It presents a preliminary analysis of an estimator of a quantity that every variational inference researcher would want to know about. The mathematical exposition is good: the authors promise more technical and theoretical studies down the road. The experimental study is the weakest point of the paper, where they miss the opportunity to explore practical aspects of their estimator (specifically, other integration techniques beyond Gaussian quadrature). Overall it is a good paper.