Local Distribution Obfuscation via Probability Coupling

Abstract

We introduce a general model for the local obfuscation of probability distributions by probabilistic perturbation, e.g., by adding differentially private noise, and investigate its theoretical properties. Specifically, we relax a notion of distribution privacy (DistP) by generalizing it to divergence, and propose local obfuscation mechanisms that provide divergence distribution privacy. To provide f -divergence distribution privacy, we prove that probabilistic perturbation noise should be added proportionally to the Earth mover's distance between the probability distributions that we want to make indistinguishable. Furthermore, we introduce a local obfuscation mechanism, which we call a coupling mechanism, that provides divergence distribution privacy while optimizing the utility of obfuscated data by using exact/approximate auxiliary information on the input distributions we want to protect.in the scenario (i), an f -privacy mechanism can provide fdivergence DistP. Section VI generalizes DistP to use exact/approximate information on the input distribution in the scenario (ii), and proposes a local mechanism for providing DistP while optimizing utility. Section VII discusses related work and Section VIII concludes.

Evaluation of Noise Distributions for Additive and Multiplicative Smart Meter Data Obfuscation

“…In [28], the authors used Laplace distribution and showed that by temporally smoothing the aggregated data, a group size of the order of thousands of SMs is sufficient for estimation of aggregated consumption. The authors in [29] introduced a model for local obfuscation of probability distribution by probability perturbation, which perturbed each single "point" datum by adding controlled probabilistic noise before sending it out to a data collector. The authors in [30] studied noise addition as a data privacy providing technique.…”

SoK: Differential privacies

“…Indeed, many definitions mentioned in this section were actually introduced with a δ parameter allowing for a small probability of error. One particularly general example is adjacency relation divergence DP [97], which combines an arbitrary neighborhood definition (like in generic DP) with an arbitrary divergence function (like in divergence DP).…”

“…For example, in [107], the author proposes endogeneous DP, which is a combination of (ε, δ)-DP and personalized DP. Similarly, pseudo-metric DP, defined in [36], is a combination of d D -privacy and (ε, δ)-DP; while extended divergence DP [97] combines d D -privacy with divergence DP.…”

“…Further relaxations encompassing the introduced dimensions are probabilistic distribution privacy 12 (combination of distribution privacy and probabilistic DP), extended distribution privacy [98] (combination of distribution privacy and d D -privacy), divergence distribution privacy [97] (combination of distribution privacy and divergence DP), extended divergence distribution privacy [97] (combination of the latter two options), and divergence distribution privacy with auxiliary inputs [97] which considers the setting where the attacker uses full or approximate knowledge rather than perfect knowledge on the input probability distributions (as in profile-based privacy).…”

“…Another option is the shuffled model [15], which falls in-between the local and global models. Some definitions we listed actually were presented in the local model, such as d D -privacy [22], geoindistinguishability [6], earth mover's Pr [68], location Pr [60], profile-based DP [73], divergence DP and smooth DP from [9], utility-optimized DP [97], and ex-tended DP, distribution Pr, and extended distribution Pr from [98]. Besides these, a handful of other local DP definitions are mentioned below; a longer discussion can be found in the full version of this work (soon to be uploaded to ArXiv 15 ).…”