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We lay theoretical foundations for new database release mechanisms that allowthird-parties to construct consistent estimators of population statistics,while ensuring that the privacy of each individual contributing to the databaseis protected. The proposed framework rests on two main ideas. First, releasing(an estimate of) the kernel mean embedding of the data generating randomvariable instead of the database itself still allows third-parties to constructconsistent estimators of a wide class of population statistics. Second, thealgorithm can satisfy the definition of differential privacy by basing thereleased kernel mean embedding on entirely synthetic data points, whilecontrolling accuracy through the metric available in a Reproducing KernelHilbert Space. We describe two instantiations of the proposed framework,suitable under different scenarios, and prove theoretical results guaranteeingdifferential privacy of the resulting algorithms and the consistency ofestimators constructed from their outputs.

Differentially Private Database Release via Kernel Mean Embeddings