  We propose a general approach for differentially private synthetic data
generation, that consists of three steps: (1) select a collection of
low-dimensional marginals, (2) measure those marginals with a noise addition
mechanism, and (3) generate synthetic data that preserves the measured
marginals well. Central to this approach is Private-PGM, a post-processing
method that is used to estimate a high-dimensional data distribution from noisy
measurements of its marginals. We present two mechanisms, NIST-MST and MST,
that are instances of this general approach. NIST-MST was the winning mechanism
in the 2018 NIST differential privacy synthetic data competition, and MST is a
new mechanism that can work in more general settings, while still performing
comparably to NIST-MST. We believe our general approach should be of broad
interest, and can be adopted in future mechanisms for synthetic data
generation.
