Local differential privacy (LDP) can provide each user with strong privacy guarantees under untrusted data curators while ensuring accurate statistics derived from privatized data. Due to its powerfulness, LDP has been widely adopted to protect privacy in various tasks (e.g., heavy hitters discovery, probability estimation) and systems (e.g., Google Chrome, Apple iOS). Although @math -LDP has been proposed for many years, the more general notion of @math -LDP has only been studied in very few papers, which mainly consider mean estimation for numeric data. Besides, prior solutions achieve @math -LDP by leveraging Gaussian mechanism, which leads to low accuracy of the aggregated results. In this paper, we propose novel mechanisms that achieve @math -LDP with high utility in data analytics and machine learning. Specifically, we first design @math -LDP algorithms for collecting multi-dimensional numeric data, which can ensure higher accuracy than the optimal Gaussian mechanism while guaranteeing strong privacy for each user. Then, we investigate different local protocols for categorical attributes under @math -LDP. Furthermore, we conduct theoretical analysis on the error bound and variance of the proposed algorithms. Experimental results on real and synthetic datasets demonstrate the high data utility of our proposed algorithms on both simple data statistics and complex machine learning models.
In the setting of @math -LDP , Gaboardi @cite_23 have investigated the upper and lower error bounds of mean estimation when protecting privacy by adding Gaussian noise. Afterward, Joseph @cite_60 further provided a smaller lower bound of mean estimation than Gaboardi @cite_23 . As for heavy hitter discovery problem, Bun @cite_53 have focused on the transformation of approximate local private protocol ( @math -LDP ) into a pure local private protocol ( @math -LDP ). Moreover, under the constraint of @math -LDP , Bassily @cite_34 proposed algorithms for estimating a set of linear queries in both offline setting and adaptive setting and analyzed the accuracy bound of the proposed algorithms. So far, the above mechanisms under @math -LDP are all achieved by the classical Gaussian mechanism @cite_32 , which yields low accuracies of the estimation results. Thus, the goal of this paper is to investigate the mechanisms which can achieve @math -LDP with higher accuracies on estimation results.
@cite_60 @cite_53 @cite_32 @cite_23 @cite_34
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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. Local differential privacy (LDP), where each user perturbs her data locally before sending to an untrusted data collector, is a new and promising technique for privacy-preserving distributed data collection. The advantage of LDP is to enable the collector to obtain accurate statistical estimation on sensitive user data (e.g., location and app usage) without accessing them. However, existing work on LDP is limited to simple data types, such as categorical, numerical, and set-valued data. To the best of our knowledge, there is no existing LDP work on key-value data, which is an extremely popular NoSQL data model and the generalized form of set-valued and numerical data. In this paper, we study this problem of frequency and mean estimation on key-value data by first designing a baseline approach PrivKV within the same "perturbation-calibration" paradigm as existing LDP techniques. To address the poor estimation accuracy due to the clueless perturbation of users, we then propose two iterative solutions PrivKVM and PrivKVM+ that can gradually improve the estimation results through a series of iterations. An optimization strategy is also presented to reduce network latency and increase estimation accuracy by introducing virtual iterations in the collector side without user involvement. We verify the correctness and effectiveness of these solutions through theoretical analysis and extensive experimental results. We study a basic private estimation problem: each of @math users draws a single i.i.d. sample from an unknown Gaussian distribution, and the goal is to estimate the mean of this Gaussian distribution while satisfying local differential privacy for each user. Informally, local differential privacy requires that each data point is individually and independently privatized before it is passed to a learning algorithm. Locally private Gaussian estimation is therefore difficult because the data domain is unbounded: users may draw arbitrarily different inputs, but local differential privacy nonetheless mandates that different users have (worst-case) similar privatized output distributions. We provide both adaptive two-round solutions and nonadaptive one-round solutions for locally private Gaussian estimation. We then partially match these upper bounds with an information-theoretic lower bound. This lower bound shows that our accuracy guarantees are tight up to logarithmic factors for all sequentially interactive @math -locally private protocols. We present a new locally differentially private algorithm for the heavy hitters problem which achieves optimal worst-case error as a function of all standardly considered parameters. Prior work obtained error rates which depend optimally on the number of users, the size of the domain, and the privacy parameter, but depend sub-optimally on the failure probability. We strengthen existing lower bounds on the error to incorporate the failure probability, and show that our new upper bound is tight with respect to this parameter as well. Our lower bound is based on a new understanding of the structure of locally private protocols. We further develop these ideas to obtain the following general results beyond heavy hitters. (1) Advanced Grouposition: In the local model, group privacy for k users degrades proportionally to root k, instead of linearly in k as in the central model. Stronger group privacy yields improved max-information guarantees, as well as stronger lower bounds (via "packing arguments"), over the central model. (2) Building on a transformation of Bassily and Smith (STOC 2015), we give a generic transformation from any non-interactive approximate-private local protocol into a pure-private local protocol. Again in contrast with the central model, this shows that we cannot obtain more accurate algorithms by moving from pure to approximate local privacy.