Log-Concave and Multivariate Canonical Noise Distributions for Differential Privacy. (arXiv:2206.04572v2 [cs.CR] UPDATED)

A canonical noise distribution (CND) is an additive mechanism designed to
satisfy $f$-differential privacy ($f$-DP), without any wasted privacy budget.
$f$-DP is a hypothesis testing-based formulation of privacy phrased in terms of
tradeoff functions, which captures the difficulty of a hypothesis test. In this
paper, we consider the existence and construction of both log-concave CNDs and
multivariate CNDs. Log-concave distributions are important to ensure that
higher outputs of the mechanism correspond to higher input values, whereas
multivariate noise distributions are …

canonical differential privacy distributions log privacy