Local Obfuscation Mechanisms for Hiding Probability Distributions

Abstract

We introduce a formal model for the information leakage of probability distributions and define a notion called distribution privacy as the local differential privacy for probability distributions. Roughly, the distribution privacy of a local obfuscation mechanism means that the attacker cannot significantly gain any information on the distribution of the mechanism's input by observing its output. Then we show that existing local mechanisms can hide input distributions in terms of distribution privacy, while deteriorating the utility by adding too much noise. For example, we prove that the Laplace mechanism needs to add a large amount of noise proportionally to the infinite Wasserstein distance between the two distributions we want to make indistinguishable. To improve the tradeoff between distribution privacy and utility, we introduce a local obfuscation mechanism, called a tupling mechanism, that adds random dummy data to the output. Then we apply this mechanism to the protection of user attributes in location based services. By experiments, we demonstrate that the tupling mechanism outperforms popular local mechanisms in terms of attribute obfuscation and service quality.

Local Distribution Obfuscation via Probability Coupling

“…The two kinds of composition have been studies in previous work (e.g., [19], [6]). For two mechanisms A 0 and A 1 , the composition A 1 ⊙ A 0 means that an identical input value x is given to two DistP mechanisms A 0 and A 1 , whereasA 1 • A 0 means that independent inputs x b are provided to mechanisms A b .…”

“…As for pre-processing, we use the following definition of stability [6], which is analogous to the stability for DP.…”

“…Recent researches [5], [6], [7] show that local obfuscation mechanisms can be used to hide the probability distributions that lie behind such point data and implicitly represent sensitive attributes (e.g., age, gender, social status). In particular, [6] proposes the notion of distribution privacy (DistP) as the local DP of probability distributions. Roughly, DistP of a local obfuscation mechanism A represents that the adversary cannot significantly gain information on the distribution of A's input by observing A's output.…”

Profile-based Privacy for Locally Private Computations

“…Another closely related concurrent independent work is DistP [11]. This work also defines a privacy notion over a set of adjacencies across data distributions.…”

“…Additionally, they explore extended privacy frameworks that intorduce metrics into the guarantees, much like geoindistinguishability. Our work is mainly complementary to [11]. We focus instead on discrete settings where the specific structure of our profile adjacency graph can be exploited, as well as finding mechanisms that achieve privacy guarantees without explicit metrics or additive δ terms.…”