Integer Subspace Differential Privacy

We propose new differential privacy solutions for when external invariants and integer constraints are simultaneously enforced on the data product. These requirements arise in real world applications of private curation, including public release 2020 U.S. Decennial Census. They pose a great challenge to production provably products with adequate statistical usability. subspace rigorously articulate guarantee maintain both characteristics, demonstrate composition post-processing properties our proposal. To address sampling from potentially highly restricted discrete space, we devise pair unbiased additive mechanisms, generalized Laplace Gaussian by solving Diophantine equations as defined constraints. The proposed mechanisms have good accuracy, errors exhibiting sub-exponential sub-Gaussian tail probabilities respectively. implement proposal, design an MCMC algorithm supply empirical convergence assessment using estimated upper bounds total variation distance via L-lag coupling. efficacy proposal synthetic problem intersecting invariants, sensitive contingency table known margins, 2010 Census county-level demonstration mandated fixed state population totals.