Differential Privacy Preserving Spectral Graph Analysis

With the increasing prevalence of information networks, research on privacy-preserving network data publishing has received substantial attention recently. There are two streams of relevant research, targeting different privacy requirements. A large body of existing works focus on preventing node re-identification against adversaries with structural background knowledge, while some other studies aim to thwart edge disclosure. In general, the line of research on preventing edge disclosure is less fruitful, largely due to lack of a formal privacy model. The recent emergence of differential privacy has shown great promise for rigorous prevention of edge disclosure. Yet recent research indicates that differential privacy is vulnerable to data correlation, which hinders its application to network data that may be inherently correlated. In this paper, we show that differential privacy could be tuned to provide provable privacy guarantees even in the correlated setting by introducing an extra parameter, which measures the extent of correlation. We subsequently provide a holistic solution for non-interactive network data publication. First, we generate a private vertex labeling for a given network dataset to make the corresponding adjacency matrix form dense clusters. Next, we adaptively identify dense regions of the adjacency matrix by a data-dependent partitioning process. Finally, we reconstruct a noisy adjacency matrix by a novel use of the exponential mechanism. To our best knowledge, this is the first work providing a practical solution for publishing real-life network data via differential privacy. Extensive experiments demonstrate that our approach performs well on different types of real-life network datasets.

Federated learning is a distributed machine learning technique that allows multiple devices to collaborate on learning a shared model without exchanging data. It can be used to improve model accuracy while protecting user privacy. However, traditional federated learning is vulnerable to attacks from generative adversarial networks (GANs). As a new privacy protection method, differential privacy enhances privacy protection capabilities by sacrificing some data accuracy. To optimize the privacy budget allocation scheme in traditional differential privacy, we propose a differential privacy method called ADP-FL, which dynamically adjusts the privacy budget based on Newton’s Law of Cooling. While maintaining the overall privacy budget, it dynamically tunes adaptive parameters to improve training accuracy. Additionally, we propose an asynchronous federated learning aggregation scheme that combines privacy budget with data freshness, thereby reducing the impact of differential privacy on accuracy. We conducted extensive experiments on differential privacy algorithms based on Gaussian mechanisms and Laplace mechanisms. The experimental results show that, under the same privacy budget, our algorithm achieves higher accuracy and lower communication overhead compared to the baseline algorithm.

The macro nature of social networks has always been a hot topic of scientific research, which is of great help in studying the characteristics of human social behavior. The spectrum is closely related to the nature of the network and determines certain information, including community division, loop, diameter, degree and so on. To ensure the security of data, the differential privacy security framework is used to propose three algorithms for privacy protection of edge weights in spectrum query. Firstly, the basic concepts of edge weight neighbor graph and edge weight difference privacy are given. For the single singular value query, the L1 global sensitivity of the function is proved, and an algorithm satisfying ε-differential privacy is designed by using Laplace mechanism. It can guarantee the privacy of edge weights when we query someone singular value. However, it cannot provide reasonable privacy protection for multiple singular value queries. So the L2 global sensitivity of the query for multiple singular values is further proved, and the Gaussian mechanism is used to design an algorithm that satisfies (ε, δ)-differential privacy. Finally, to combine with multi-singular values query strategy and spectral decomposition, a novel graph data publishing algorithm which can guarantee edge weight (ε, δ)-differential privacy is proposed. To verify the availability of these methods, experimental tests have been carried out in both model networks and actual networks, which shows that the algorithm can better guarantee the availability of data.

How to achieve differential privacy in the distributed setting, where the dataset is distributed among the istrustful parties, is an important problem. We consider in what condition can a protocol inherit the differential privacy property of a function it computes. The heart of the problem is the secure multiparty computation of randomized function. A notion obliviousness is introduced, which captures the key security problems when computing a randomized function from a deterministic one in the distributed setting. By this observation, a sufficient and necessary condition about securely computing a randomized function from a deterministic one is given. The above result can not only be used to determine whether a protocol computing differentially private function is secure, but also be used to construct a secure one. Then we prove that the differential privacy property of a function can be inherited by the protocol computing it if the protocol securely computes it. A composition theorem of differentially private protocols is also presented. Finally, we construct protocols of Gaussian mechanism and Laplace mechanism, which inherit the differential privacy property.

The existing privacy protection schemes for Location‐Based Service (LBS) only protect users' location privacy or query privacy, which can not adopt both of the privacy protections simultaneously in the LBS system. Moreover, these schemes cannot take into account the spatial‐temporal correlation and background knowledge. In response to the above mentioned questions, the LBS Privacy Protection Scheme Based on Differential Privacy (DPLQ) is proposed. The method contains two kinds of privacy protection algorithms: users' location privacy protection algorithm and users' query privacy protection algorithm. The users' location privacy protection algorithm divides the map using the Voronoi diagram, choosing l fake location points based on the improved k ‐means algorithm and l ‐diversity idea, and protects users' location privacy with the Laplace mechanism. Based on the k ‐anonymous algorithm, the users' query privacy protection algorithm builds a query k ‐anonymous set according to the neighbour users' query requests at the same time t in the cluster and the historical query probability of the region’s POI and protects users' query privacy with the exponential mechanism. Through setting the privacy protection intensity of the algorithm by the users, the generated location dataset and query k ‐anonymous set can resist a variety of attacks from malicious attackers. Theoretical analysis and experimental results show that the scheme can effectively protect the location privacy and query privacy of users.

With the continuous development of artificial intelligence technology, machine learning in distributed network systems, such as IoVflntemet of Vehicles), will inevitably lead to privacy leakage. At present, there are lots of problems in federated learning, differential privacy and other machine learning privacy protection schemes, such as high loss of availability and the need of a fully trusted third-party server. In order to solve these problems, we propose MDPFL(Multiple Differential Privacy based on Federated Learning) algorithm. The algorithm combines with the differential privacy model in each stage of federated learning to solve the problem of curious third-party data collectors obtaining users’ original data in the process of machine learning. Meanwhile, the algorithm does not adopt a decentralized machine learning scheme directly, but uses a double noise adding mode with the existence of the third-party data collectors. We use Laplacian mechanism in the central server and GRR mechanism in local clients to ensure the goal of stability of the effect of the machine ¡earning model. The algorithm is compared with FedAvg, CDP, LDP algorithm in accuracy and loss rate which based on EMNIST data sets. In different global sensitivities, the model training effect is consistent with FedAvg algorithm while comparing with LDP algorithm, the speed of model convergence is improved.

Private record linkage (PRL) is the problem of identifying pairs of records that are similar as per an input matching rule from databases held by two parties that do not trust one another. We identify three key desiderata that a PRL solution must ensure: (1) perfect precision and high recall of matching pairs, (2) a proof of end-to-end privacy, and (3) communication and computational costs that scale subquadratically in the number of input records. We show that all of the existing solutions for PRL? including secure 2-party computation (S2PC), and their variants that use non-private or differentially private (DP) blocking to ensure subquadratic cost -- violate at least one of the three desiderata. In particular, S2PC techniques guarantee end-to-end privacy but have either low recall or quadratic cost. In contrast, no end-to-end privacy guarantee has been formalized for solutions that achieve subquadratic cost. This is true even for solutions that compose DP and S2PC: DP does not permit the release of any exact information about the databases, while S2PC algorithms for PRL allow the release of matching records. In light of this deficiency, we propose a novel privacy model, called output constrained differential privacy, that shares the strong privacy protection of DP, but allows for the truthful release of the output of a certain function applied to the data. We apply this to PRL, and show that protocols satisfying this privacy model permit the disclosure of the true matching records, but their execution is insensitive to the presence or absence of a single non-matching record. We find that prior work that combine DP and S2PC techniques even fail to satisfy this end-to-end privacy model. Hence, we develop novel protocols that provably achieve this end-to-end privacy guarantee, together with the other two desiderata of PRL. Our empirical evaluation also shows that our protocols obtain high recall, scale near linearly in the size of the input databases and the output set of matching pairs, and have communication and computational costs that are at least 2 orders of magnitude smaller than S2PC baselines.

Differential privacy is a statistical definition of privacy that has attracted the interest of both academia and industry. Its formulations are easy to understand, but the differential privacy of databases is complicated to determine. One of the reasons for this is that small changes in database programs can break their differential privacy. Therefore, formal verification of differential privacy has been studied for over a decade. In this paper, we propose an Isabelle/HOL library for formalizing differential privacy in a general setting. To our knowledge, it is the first formalization of differential privacy that supports continuous probability distributions. First, we formalize the standard definition of differential privacy and its basic properties. Second, we formalize the Laplace mechanism and its differential privacy. Finally, we formalize the differential privacy of the report noisy max mechanism.

Network data often contain sensitive relational information. One approach to protecting sensitive information while offering flexibility for network analysis is to share synthesized networks based on the information in originally observed networks. We employ differential privacy (DP) and exponential random graph models (ERGMs) and propose the DP-ERGM method to synthesize network data. We apply DP-ERGM to two real-world networks. We then compare the utility of synthesized networks generated by DP-ERGM, the DyadWise Randomized Response (DWRR) approach, and the Synthesis through Conditional distribution of Edge given nodal Attribute (SCEA) approach. In general, the results suggest that DP-ERGM preserves the original information significantly better than two other approaches in network structural statistics and inference for ERGMs and latent space models. Furthermore, DP-ERGM satisfies node DP through modeling the global network structure with ERGM, a stronger notion of privacy than the edge DP under which DWRR and SCEA operate.

Differential privacy protection scheme based on community density aggregation and matrix perturbation

Recent years have witnessed growing concerns about the privacy of sensitive data. In response to these concerns, differential privacy has emerged as a rigorous framework for privacy protection, gaining widespread recognition in both academic and industrial domains. While substantial progress has been made in private data analysis, existing methods often suffer from impracticality or a significant loss of statistical efficiency. This article aims to alleviate these concerns in the context of hypothesis testing by introducing differentially private permutation tests. The proposed framework extends classical non-private permutation tests to private settings, maintaining both finite-sample validity and differential privacy in a rigorous manner. The power of the proposed test depends on the choice of a test statistic, and we establish general conditions for consistency and non-asymptotic uniform power. To demonstrate the utility and practicality of our framework, we focus on reproducing kernel-based test statistics and introduce differentially private kernel tests for two-sample and independence testing: dpMMD and dpHSIC . The proposed kernel tests are straightforward to implement, applicable to various types of data, and attain minimax optimal power across different privacy regimes. Our empirical evaluations further highlight their competitive power under various synthetic and real-world scenarios, emphasizing their practical value. The code is publicly available to facilitate the implementation of our framework. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Semi-structured business processes are emerging at a rapid pace in industries such as government, insurance, banking and healthcare. The workflows underlying these case-oriented processes are non-deterministic. They are mostly driven by human decision making and content status and they may change frequently depending on factors such as economic conditions, legislative policy changes and technological upgrades. This paper describes a method to detect changes in a running business process by conducting spectral graph analysis of sets of execution traces of the process. This method is beneficial because it does not require mining a process model of the business process, and is consequently independent of any assumptions about the nature of the business process. This makes it particularly applicable to case-oriented semi-structured business processes whose lifecycle is not fully driven by a formal process model. In this paper we present our algorithm for computing graph spectra from business process execution traces, and discuss some initial promising results, as well as exciting ideas generated by this research for future work.

We propose a fundamentally new approach to Datalog evaluation. Given a linear Datalog program DB written usingNconstants and binary predicates, we first translate if-and-only-if completions of clauses in DB into a setEq(DB) of matrix equations with a non-linear operation, where relations inMDB, the least Herbrand model of DB, are encoded as adjacency matrices. We then translateEq(DB) into another, but purely linear matrix equationsẼq(DB). It is proved that the least solution ofẼq(DB) in the sense of matrix ordering is converted to the least solution ofEq(DB) and the latter givesMDBas a set of adjacency matrices. Hence, computing the least solution ofẼq(DB) is equivalent to computingMDBspecified by DB. For a class of tail recursive programs and for some other types of programs, our approach achievesO(N3) time complexity irrespective of the number of variables in a clause since only matrix operations costingO(N3) or less are used. We conducted two experiments that compute the least Herbrand models of linear Datalog programs. The first experiment computes transitive closure of artificial data and real network data taken from the Koblenz Network Collection. The second one compared the proposed approach with the state-of-the-art symbolic systems including two Prolog systems and two ASP systems, in terms of computation time for a transitive closure program and the same generation program. In the experiment, it is observed that our linear algebraic approach runs 101~ 104times faster than the symbolic systems when data is not sparse. Our approach is inspired by the emergence of big knowledge graphs and expected to contribute to the realization of rich and scalable logical inference for knowledge graphs.

Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency matrix) description of the network structure. While extensive approaches---such as the state-of-the-art Message Passing Approach---typically yield more accurate predictions, intensive approaches provide crucial insights on the role played by any given structural property in the outcome of dynamical processes. Here we introduce an intensive description that yields almost identical predictions to the ones obtained with MPA for bond percolation. Our approach distinguishes nodes according to two simple statistics: their degree and their position in the core-periphery organization of the network. Our near-exact predictions highlight how accurately capturing the long-range correlations in network structures allows to easily and effectively compress real complex network data.

Differential privacy has become a crucial tool for protecting sensitive information. In network data, both the existence of edges and their associated covariates may reveal private details, making their unprotected release a serious privacy concern. However, most existing approaches to edge privacy fail to account for the protection of edge-specific covariates. In this paper, we address this gap by proposing a unified framework for safeguarding both edges and edge-wise covariates in covariate-assisted network models. We introduce edge-covariate differential privacy, a privacy notion designed to simultaneously protect the presence of edges and their associated covariates. To assess its impact on network modeling, we investigate the fundamental privacy–utility tradeoff of parameter estimation under a joint latent space model. Our approach employs a mixed privatization mechanism that combines randomized response for edges with a Laplace mechanism for covariates. We establish asymptotic consistency and minimax optimality, up to logarithmic factors, for parameter estimation under this privacy constraint. Extensive simulation studies and an application to a real-world citation network demonstrate that our method achieves a favorable balance between strong privacy guarantees and estimation accuracy.