Generalised Likelihood Ratio Testing Adversaries through the Differential Privacy Lens
arXiv preprint arXiv:2210.13028, 2022•arxiv.org
Differential Privacy (DP) provides tight upper bounds on the capabilities of optimal
adversaries, but such adversaries are rarely encountered in practice. Under the hypothesis
testing/membership inference interpretation of DP, we examine the Gaussian mechanism
and relax the usual assumption of a Neyman-Pearson-Optimal (NPO) adversary to a
Generalized Likelihood Test (GLRT) adversary. This mild relaxation leads to improved
privacy guarantees, which we express in the spirit of Gaussian DP and $(\varepsilon,\delta) …
adversaries, but such adversaries are rarely encountered in practice. Under the hypothesis
testing/membership inference interpretation of DP, we examine the Gaussian mechanism
and relax the usual assumption of a Neyman-Pearson-Optimal (NPO) adversary to a
Generalized Likelihood Test (GLRT) adversary. This mild relaxation leads to improved
privacy guarantees, which we express in the spirit of Gaussian DP and $(\varepsilon,\delta) …
Differential Privacy (DP) provides tight upper bounds on the capabilities of optimal adversaries, but such adversaries are rarely encountered in practice. Under the hypothesis testing/membership inference interpretation of DP, we examine the Gaussian mechanism and relax the usual assumption of a Neyman-Pearson-Optimal (NPO) adversary to a Generalized Likelihood Test (GLRT) adversary. This mild relaxation leads to improved privacy guarantees, which we express in the spirit of Gaussian DP and -DP, including composition and sub-sampling results. We evaluate our results numerically and find them to match the theoretical upper bounds.
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