Post-processing differentially private counts to satisfy additive constraints
To reduce disclosure risks, statistical agencies and other organizations can release noisy counts that satisfy differential privacy. In some contexts, the released counts satisfy additive con-straints; for example, the released value of a total should equal the sum of the released values of its components. We present a simple post-processing procedure for satisfying such additive constraints. The basic idea is (i) compute approximate posterior modes of the true counts given the noisy counts, (ii) construct a multinomial distribution with trial size equal to the posterior mode of the total and probability vector equal to fractions derived from the posterior modes of the components, and (iii) find and release a mode of this multinomial distribution. We also present an approach for making Bayesian inferences about the true counts given these post-processed, differentially private counts. We illustrate these methods using simulations.
