We show that it is possible to significantly improve the accu-racy of a general class of histogram queries while satisfying differential privacy. Our approach carefully chooses a set of queries to evaluate, and then exploits consistency con-straints that should hold over the noisy output. In a post-processing phase, we compute the consistent input most likely to have produced the noisy output. The final out-put is differentially-private and consistent, but in addition, it is often much more accurate. We show, both theoreti-cally and experimentally, that these techniques can be used for estimating the degree sequence of a graph very precisely, and for computing a histogram that can support arbitrary range queries accurately.
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