Biblio
In local differential privacy (LDP), each user perturbs her data locally before sending the noisy data to a data collector. The latter then analyzes the data to obtain useful statistics. Unlike the setting of centralized differential privacy, in LDP the data collector never gains access to the exact values of sensitive data, which protects not only the privacy of data contributors but also the collector itself against the risk of potential data leakage. Existing LDP solutions in the literature are mostly limited to the case that each user possesses a tuple of numeric or categorical values, and the data collector computes basic statistics such as counts or mean values. To the best of our knowledge, no existing work tackles more complex data mining tasks such as heavy hitter discovery over set-valued data. In this paper, we present a systematic study of heavy hitter mining under LDP. We first review existing solutions, extend them to the heavy hitter estimation, and explain why their effectiveness is limited. We then propose LDPMiner, a two-phase mechanism for obtaining accurate heavy hitters with LDP. The main idea is to first gather a candidate set of heavy hitters using a portion of the privacy budget, and focus the remaining budget on refining the candidate set in a second phase, which is much more efficient budget-wise than obtaining the heavy hitters directly from the whole dataset. We provide both in-depth theoretical analysis and extensive experiments to compare LDPMiner against adaptations of previous solutions. The results show that LDPMiner significantly improves over existing methods. More importantly, LDPMiner successfully identifies the majority true heavy hitters in practical settings.
Given a set D of tuples defined on a domain Omega, we study differentially private algorithms for constructing a histogram over Omega to approximate the tuple distribution in D. Existing solutions for the problem mostly adopt a hierarchical decomposition approach, which recursively splits Omega into sub-domains and computes a noisy tuple count for each sub-domain, until all noisy counts are below a certain threshold. This approach, however, requires that we (i) impose a limit h on the recursion depth in the splitting of Omega and (ii) set the noise in each count to be proportional to h. The choice of h is a serious dilemma: a small h makes the resulting histogram too coarse-grained, while a large h leads to excessive noise in the tuple counts used in deciding whether sub-domains should be split. Furthermore, h cannot be directly tuned based on D; otherwise, the choice of h itself reveals private information and violates differential privacy. To remedy the deficiency of existing solutions, we present PrivTree, a histogram construction algorithm that adopts hierarchical decomposition but completely eliminates the dependency on a pre-defined h. The core of PrivTree is a novel mechanism that (i) exploits a new analysis on the Laplace distribution and (ii) enables us to use only a constant amount of noise in deciding whether a sub-domain should be split, without worrying about the recursion depth of splitting. We demonstrate the application of PrivTree in modelling spatial data, and show that it can be extended to handle sequence data (where the decision in sub-domain splitting is not based on tuple counts but a more sophisticated measure). Our experiments on a variety of real datasets show that PrivTree considerably outperforms the states of the art in terms of data utility.