  Many privacy mechanisms reveal high-level information about a data
distribution through noisy measurements. It is common to use this information
to estimate the answers to new queries. In this work, we provide an approach to
solve this estimation problem efficiently using graphical models, which is
particularly effective when the distribution is high-dimensional but the
measurements are over low-dimensional marginals. We show that our approach is
far more efficient than existing estimation techniques from the privacy
literature and that it can improve the accuracy and scalability of many
state-of-the-art mechanisms.
