In this paper, we evaluate empirically the quality of statistical inference from differentially-private synthetic contingency tables. We compare three methods: histogram perturbation, the Dirichlet-Multinomial synthesizer and the Hardt-Ligett-McSherry algorithm. We consider a goodness-of-fit test for models suitable to the real data, and a model selection procedure. We find that the theoretical guarantees associated with these differentially-private datasets do not always translate well into guarantees about the statistical inference on the synthetic datasets.
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