SoK: Descriptive Statistics Under Local Differential Privacy

With the advent of the era of big data, privacy issues have been becoming a hot topic in public. Local differential privacy (LDP) is a state-of-the-art privacy preservation technique that allows to perform big data analysis (e.g., statistical estimation, statistical learning, and data mining) while guaranteeing each individual participant’s privacy. In this paper, we present a comprehensive survey of LDP. We first give an overview on the fundamental knowledge of LDP and its frameworks. We then introduce the mainstream privatization mechanisms and methods in detail from the perspective of frequency oracle and give insights into recent studied on private basic statistical estimation (e.g., frequency estimation and mean estimation) and complex statistical estimation (e.g., multivariate distribution estimation and private estimation over complex data) under LDP. Furthermore, we present current research circumstances on LDP including the private statistical learning/inferencing, private statistical data analysis, privacy amplification techniques for LDP, and some application fields under LDP. Finally, we identify future research directions and open challenges for LDP. This survey can serve as a good reference source for the research of LDP to deal with various privacy-related scenarios to be encountered in practice.

Local differential privacy (LDP) provides a way for an untrusted data collector to aggregate users' data without violating their privacy. Various privacy-preserving data analysis tasks have been studied under the protection of LDP, such as frequency estimation, frequent itemset mining, and machine learning. Despite its privacy-preserving properties, recent research has demonstrated the vulnerability of certain LDP protocols to data poisoning attacks. However, existing data poisoning attacks are focused on basic statistics under LDP, such as frequency estimation and mean/variance estimation. As an important data analysis task, the security of LDP frequent itemset mining has yet to be thoroughly examined. In this paper, we aim to address this issue by presenting novel and practical data poisoning attacks against LDP frequent itemset mining protocols. By introducing a unified attack framework with composable attack operations, our data poisoning attack can successfully manipulate the state-of-the-art LDP frequent itemset mining protocols and has the potential to be adapted to other protocols with similar structures. We conduct extensive experiments on three datasets to compare the proposed attack with four baseline attacks. The results demonstrate the severity of the threat and the effectiveness of the proposed attack.

Some Thoughts About Data Type, Distribution, and Statistical Significance

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) has been widely recognized as a powerful tool for providing a strong theoretical guarantee of data privacy to data contributors against an untrusted data collector. Under a typical LDP scheme, each data contributor independently randomly perturbs their data before submitting them to the data collector, which in turn infers valuable statistics about the original data from received perturbed data. Common to existing LDP mechanisms is an inherent trade-off between the level of privacy protection and data utility in the sense that strong data privacy often comes at the cost of reduced data utility. Frequency estimation based on Randomized Response (RR) is a fundamental building block of many LDP mechanisms. In this paper, we propose a novel Joint Randomized Response (JRR) mechanism based on correlated data perturbations to achieve locally differentially private frequency estimation. JRR divides data contributors into disjoint groups of two members and lets those in the same group jointly perturb their binary data to improve frequency-estimation accuracy and achieve the same level of data privacy by hiding the group membership information in contrast to the classical RR mechanism. Theoretical analysis and detailed simulation studies using both real and synthetic datasets show that JRR achieves the same level of data privacy as the classical RR mechanism while improving the frequency-estimation accuracy in the overwhelming majority of the cases by up to two orders of magnitude.

Local differential privacy (LDP) is a promising privacy model for data collection that protects sensitive information of individuals. However, applying LDP to top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> estimation in set-valued data (e.g., identifying most frequent <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> items) may yield poor results for small and sparse datasets due to high sensitivity and heavy perturbation. To address this, we propose an adaptive approach that frames the problem as a multi-armed bandit (MAB) problem, in which the decision-maker selects actions based on information collected from previous rounds to maximize the total reward over time. Inspired by this, we present two adaptive sampling schemes based on MAB: <b>ARBS</b> for identifying top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> items and <b>ARBSF</b> for both top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> item discovery and frequency estimation on these items. Furthermore, to address the potential long delay of multi-round collection, we propose an optimization technique to reduce the time complexity. Both theoretical and empirical results show that our adaptive sampling schemes significantly outperform existing alternatives.

This paper describes an improved method of the variance estimation of Gaussian distribution for Histogram Matching based on Gaussian Distribution (HMGD). In our previous paper, focusing on the symmetry of the Gaussian function, we presented another method for the variance (or Gaussian width) estimation of Gaussian distribution in the original histogram. However, since the real shape of mountain like Gaussian function in the original image’s histogram does not always show the good symmetry, the variance estimation method that we previously presented did not work so well as we expected. In this paper, we newly propose the improved estimation method using regression analysis, based on curvature computation for the cumulative histogram of original image’s one. In the newly proposed method, first, we detect the histogram peak of original image’s histogram by using curvature computation; next, we perform the regression analysis for the cumulative histogram, using an approximated function of the curvature that includes the variance parameter. Also in this paper, we show some experimental results by the estimation method.

There have been a significant number of recent papers about hyperspectral imaging, which propose various methods for estimating the number of materials/endmembers in hyperspectral images. This is sometimes called the “intrinsic” dimension (ID) of the image. Estimation of the error variance in each spectral band is a critical first step in ID estimation. The estimated error variances can then be used to preprocess (e.g., whiten) the data, prior to ID estimation. A range of variance estimation methods have been advocated in the literature. We investigate the impact of five variance estimation methods (three using spatial information and two using spectral information) on five ID estimation methods, with the aid of four different, but semirealistic, sets of simulated hyperspectral images. Our findings are as follows: first, for all four sets, the two spectral variance estimation methods significantly outperform the three spatial methods; second, when used with the spectral variance estimation methods, two of the ID estimation methods (called random matrix theory and NWHFC) consistently outperform the other three ID estimation methods; third, the better spectral variance estimation method sometimes gives negative variance estimates; fourth, we introduce a simple correction that guarantees positivity; and fifth, we give a fast algorithm for its computation.

This work compares the accuracy of fundamental frequency and formant frequency estimation methods and maximum a posteriori (MAP) prediction from MFCC vectors with hand-corrected references. Five fundamental frequency estimation methods are compared to fundamental frequency prediction from MFCC vectors in both clean and noisy speech. Similarly, three formant frequency estimation and prediction methods are compared. An analysis of estimation and prediction accuracy shows that prediction from MFCCs provides the most accurate voicing classification across clean and noisy speech. On clean speech, fundamental frequency estimation outperforms prediction from MFCCs, but as noise increases the performance of prediction is significantly more robust than estimation. Formant frequency prediction is found to be more accurate than estimation in both clean and noisy speech. A subjective analysis of the estimation and prediction methods is also made by reconstructing speech from the acoustic features.

In the context of the Internet of Things (IoT), the large-scale generation and collection of data can greatly improve the quality of service provided, but they also raise significant concerns about privacy breaches. However, existing privacy-preserving data collection solutions based on local differential privacy (LDP) often struggle to balance security and accuracy when handling composite data types. To address this challenge, in this paper, we propose CSKV, a high-precision and privacy-preserving key-value data collection scheme. Specifically, we first design a padding and sampling protocol to improve data utility. Then, we propose two randomized response mechanisms to safely perturb keys and values in a cohesive and segmented manner. After that, by leveraging the sampling protocol and key-value correlation perturbation, we demonstrate that CSKV can provide secondary privacy amplification. Detailed theoretical analysis verifies the security and effectiveness of CSKV. In addition, extensive performance evaluations are conducted on synthetic and real-world datasets, and the results indicate that our proposed scheme outperforms existing schemes in terms of hit rate and estimation variance.

A number of studies have recently been made on discrete distribution estimation in the local model, in which users obfuscate their personal data (e.g., location, response in a survey) by themselves and a data collector estimates a distribution of the original personal data from the obfuscated data. Unlike the centralized model, in which a trusted database administrator can access all users’ personal data, the local model does not suffer from the risk of data leakage. A representative privacy metric in this model is LDP (Local Differential Privacy), which controls the amount of information leakage by a parameter ∈ called privacy budget. When ∈ is small, a large amount of noise is added to the personal data, and therefore users’ privacy is strongly protected. However, when the number of users ℕ is small (e.g., a small-scale enterprise may not be able to collect large samples) or when most users adopt a small value of ∈, the estimation of the distribution becomes a very challenging task. The goal of this paper is to accurately estimate the distribution in the cases explained above. To achieve this goal, we focus on the EM (Expectation-Maximization) reconstruction method, which is a state-of-the-art statistical inference method, and propose a method to correct its estimation error (i.e., difference between the estimate and the true value) using the theory of Rilstone et al. We prove that the proposed method reduces the MSE (Mean Square Error) under some assumptions.We also evaluate the proposed method using three largescale datasets, two of which contain location data while the other contains census data. The results show that the proposed method significantly outperforms the EM reconstruction method in all of the datasets when ℕ or ∈ is small.

Many real-world social networks are decentralized in nature, and the only way to analyze such a network is to collect local views of the social graph from individual participants. Since local views may contain sensitive information, it is often desirable to apply differential privacy in the data collection process, which provides strong and rigorous privacy guarantees. In many practical situations, the local view of a participant contains not only her own connections, but also those of her neighbors, which are private and sensitive for the neighbors, but not directly so for the participant herself. We call such information beyond direct connections an extended local view (ELV), and study two fundamental problems related to ELVs: first, how do we correctly enforce differential privacy for all participants in the presence of ELVs? Second, how can the data collector utilize ELVs to obtain accurate estimates of global graph properties? This paper points out that when collecting ELVs, it is insufficient to apply a straightforward adaptation of local differential privacy (LDP), a commonly used scheme in practice, to protect the privacy of all network participants. The main problem is that an adversarial data collector can accumulate private information on a specific victim from multiple neighbors of the victim; even though the data collected from each neighbor is perturbed under LDP, their aggregate can still violate the victim's privacy. To prevent this attack, we formulate a novel decentralized differential privacy (DDP) scheme, which requires that each participant consider not only her own privacy, but also that of her neighbors involved in her ELV. The stringent privacy requirement of DDP, however, makes it challenging to design an effective mechanism for data collection. Towards this goal, we design a novel multi-phase framework under DDP that enables an analyst to accurately estimate subgraph counts, an important property of social graphs. The main idea is that instead of collecting subgraph counts directly, which would require excessively noise, the analyst first asks individuals about their respective minimum noise scale, which is private information since it depends on the local graph structure, and, thus, must be performed under DDP. For some types of subgraphs, this process is applied recursively, i.e., the analyst asks about the necessary noise to be injected into the private information on the minimum local noise scale required to protect subgraph counts under DDP. As case studies, we instantiate the proposed framework for three common subgraph patterns: triangles, three-hop paths, and k-cliques. Extensive experiments using real data demonstrate that the proposed scheme leads to accurate estimates of global subgraph counts, whereas baseline solutions fail to obtain meaningful result utility.

When collecting information, local differential privacy (LDP) alleviates privacy concerns of users because their private information is randomized before being sent it to the central aggregator. LDP imposes large amount of noise as each user executes the randomization independently. To address this issue, recent work introduced an intermediate server with the assumption that this intermediate server does not collude with the aggregator. Under this assumption, less noise can be added to achieve the same privacy guarantee as LDP, thus improving utility for the data collection task. This paper investigates this multiple-party setting of LDP. We analyze the system model and identify potential adversaries. We then make two improvements: a new algorithm that achieves a better privacy-utility tradeoff; and a novel protocol that provides better protection against various attacks. Finally, we perform experiments to compare different methods and demonstrate the benefits of using our proposed method.

Frequency estimation mechanisms are widely applied in domains such as machine learning and cloud computing, where it is desirable to provide statistical information. As a fundamental operation in these domains, frequency estimation utilizes personal data which contains sensitive information while it is necessary to protect sensitive information from others. Motivated by this, we preserve user’s privacy with local differential privacy by obfuscating personal data on the user side. In this paper, we propose frequency estimation mechanisms under utility-optimized local differential privacy (ULDP), which allow the data collector to obtain some non-sensitive values to improve data utility while protecting sensitive values from leaking sensitive information. We propose three frequency estimation mechanisms under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\epsilon ,\delta )$</tex-math></inline-formula> -ULDP (uRFM-GRR, uRFM-RAPPOR, uRFM-OLH) to preserve user’s sensitive information. Our proposed mechanisms protect sensitive data with the same privacy guarantee and they are suitable for different scenarios. Besides, in theory, we compare the estimation errors of our proposed mechanisms with existing LDP based mechanisms and show that ours are lower than theirs. Finally, we conduct experiments on synthetic and real-world datasets to evaluate the performance of the three mechanisms. The experimental results demonstrate that our proposed mechanisms are better than the existing LDP based solutions over the same privacy level, while uRFM-OLH frequently performs the best.

Nowadays, people pay more and more attention to personal privacy issues, and how to collect data while protecting personal privacy and data security has become a major challenge. Local differential privacy, as a new privacy protection model, can collect and protect user data without a trusted third party. Among the many local differential privacy algorithms, RAPPOR(Randomized Aggregatable Privacy-Preserving Ordinal Response) is suitable for situations where the privacy budget is small. However, RAPPOR uses Bloom filters to map the data, which can lead to the same encoding result for different data, and the existing solution is to group the data. The paper, we propose the digital RAPPOR algorithm D-RAPPOR (Digitization-RAPPOR) does not require grouping of user data, D-RAPPOR is based on user data on the ordinal number of candidate values The D-RAPPOR algorithm is suitable for data sets with known candidate values. In this paper, the D-RAPPOR algorithm is used for experimental analysis of electricity data, which can be collected safely. The method can obtain the individual frequencies of the customer's electricity data while ensuring the security of the customer's electricity data. The control center can analyze the results of the algorithm to achieve the purpose of regulating electricity. Finally, the algorithm proposed in this paper solves the problem that the original algorithm produces the same encoding, and the results of the D-RAPPOR algorithm are slightly better than the RAPPOR algorithm under the same privacy budget.