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Abstract:
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Differential Privacy (DP) provides a mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries. Subject to the DP constraint, it is natural to search for a procedure which maximizes the utility of the DP output relative to the standard non-private algorithms, but few works attempt to infer properties about the underlying population. In this work, we develop uniformly most powerful (UMP) tests, a concept fundamental to classical statistics, within the framework of DP. More specifically, we prove a ‘Neyman-Pearson lemma’ for binomial data under DP, from which we derive simple and one-sided UMP tests. Furthermore, we obtain exact DP p-values, by post-processing of a random variable, whose distribution we coin “Truncated-Uniform-Laplace” (Tulap), a generalization of the Staircase and discrete Laplace distributions. Our results are the first to achieve UMP tests under (?, ?)?DP, and are among the first steps towards a general theory of optimal inference under DP. (joint work with Jordan Awan)
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