  Many analysis and machine learning tasks require the availability of marginal
statistics on multidimensional datasets while providing strong privacy
guarantees for the data subjects. Applications for these statistics range from
finding correlations in the data to fitting sophisticated prediction models. In
this paper, we provide a set of algorithms for materializing marginal
statistics under the strong model of local differential privacy. We prove the
first tight theoretical bounds on the accuracy of marginals compiled under each
approach, perform empirical evaluation to confirm these bounds, and evaluate
them for tasks such as modeling and correlation testing. Our results show that
releasing information based on (local) Fourier transformations of the input is
preferable to alternatives based directly on (local) marginals.
