Canonical Noise Distributions and Private Hypothesis Tests. (arXiv:2108.04303v2 [cs.CR] UPDATED)

$f$-DP has recently been proposed as a generalization of differential privacy
allowing a lossless analysis of composition, post-processing, and privacy
amplification via subsampling. In the setting of $f$-DP, we propose the concept
of a canonical noise distribution (CND), the first mechanism designed for an
arbitrary $f$-DP guarantee. The notion of CND captures whether an additive
privacy mechanism perfectly matches the privacy guarantee of a given $f$. We
prove that a CND exists for any $f$-DP guarantee, and give a construction …

canonical tests