Heterogeneous Differential Privacy

Abstract

The massive collection of personal data by personalization systems has rendered the preservation of privacy of individuals more and more difficult. Most of the proposed approaches to preserve privacy in personalization systems usually address this issue uniformly across users, thus ignoring the fact that users have different privacy attitudes and expectations (even among their own personal data). In this paper, we propose to account for this non-uniformity of privacy expectations by introducing the concept of heterogeneous differential privacy. This notion captures both the variation of privacy expectations among users as well as across different pieces of information related to the same user. We also describe an explicit mechanism achieving heterogeneous differential privacy, which is a modification of the Laplacian mechanism by Dwork, McSherry, Nissim, and Smith. In a nutshell, this mechanism achieves heterogeneous differential privacy by manipulating the sensitivity of the function using a linear transformation on the input domain. Finally, we evaluate on real datasets the impact of the proposed mechanism with respect to a semantic clustering task. The results of our experiments demonstrate that heterogeneous differential privacy can account for different privacy attitudes while sustaining a good level of utility as measured by the recall for the semantic clustering task.

Conservative or liberal? Personalized differential privacy

“…In a very recent manuscript [3], Alaggan et al have independently developed a similar privacy notion to ours, called heterogeneous differential privacy, which to our knowledge is the only other work to consider differential privacy with non-uniform privacy guarantees. Their work differs from ours both in the presentation and in the technical contributions.…”

“…Their work differs from ours both in the presentation and in the technical contributions. In particular, the "stretching" mechanism proposed in [3], which is based on the Laplace mechanism and works by rescaling the input values according to the corresponding privacy parameters, applies only to a limited subset of realvalued functions; specifically, it cannot be used for functions like median, min/max, and many others, that rely on the exponential mechanism. It is also fundamentally incompatible with some other types of queries, such as counting the number of non-zero values in a dataset, where rescaling does not alter the answer to the query.…”

“…In contrast, our primary mechanism for achieving PDP has no such restrictions; it can be used to automatically convert any differentially private algorithm-whether it is an instance of the Laplace mechanism, the exponential mechanism or even a composition of multiple differentially private components-into one that satisfies our personalized privacy definition. Additionally, unlike [3], we present an extensive empirical analysis comparing our mechanisms to several baseline approaches to demonstrate the advantages of PDP over differential privacy, in terms of utility.…”

“…We use a slightly different definition of neighboring datasets to other sections to simplify the presentation. Here, we assume that D and D differ only in the value of a tuple t (instead of in the presence of t) 3 . We also consider datasets that have different values for an arbitrary number of tuples and will use the notation D ⊕ D to denote the set of tuples in which D and D differ.…”

“…We need to understand the structure of this function further to satisfy PDP. For any D, r, there may be many D that maximize equation (3). For instance, in the example above, we can make 5 the median by changing either 6, 9 or 11 to any value that is ≤ 5.…”