  A key challenge facing the design of differential privacy in the
non-interactive setting is to maintain the utility of the released data. To
overcome this challenge, we utilize the Diaconis-Freedman-Meckes (DFM) effect,
which states that most projections of high-dimensional data are nearly
Gaussian. Hence, we propose the RON-Gauss model that leverages the novel
combination of dimensionality reduction via random orthonormal (RON) projection
and the Gaussian generative model for synthesizing differentially-private data.
We analyze how RON-Gauss benefits from the DFM effect, and present multiple
algorithms for a range of machine learning applications, including both
unsupervised and supervised learning. Furthermore, we rigorously prove that (a)
our algorithms satisfy the strong $\epsilon$-differential privacy guarantee,
and (b) RON projection can lower the level of perturbation required for
differential privacy. Finally, we illustrate the effectiveness of RON-Gauss
under three common machine learning applications -- clustering, classification,
and regression -- on three large real-world datasets. Our empirical results
show that (a) RON-Gauss outperforms previous approaches by up to an order of
magnitude, and (b) loss in utility compared to the non-private real data is
small. Thus, RON-Gauss can serve as a key enabler for real-world deployment of
privacy-preserving data release.
