Efficiently Estimating Erdos-Renyi Graphs with Node Differential Privacy

Sealfon, Adam; Ullman, Jonathan

doi:10.48550/arxiv.1905.10477

Cited by 4 publications

(6 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[9] developed an exponential time algorithm for estimating properties in the node DP model, and derived optimal information theoretic error bounds. [35] improved this and designed a polynomial time algorithm. [22] study the problem of privacy-preserving community detection on SBMs using a simple spectral method [28] for multiple communities.…”

Section: Related Workmentioning

confidence: 99%

Differentially Private Community Detection for Stochastic Block Models

Seif¹,

Nguyen²,

Vullikanti³

et al. 2022

Preprint

View full text Add to dashboard Cite

The goal of community detection over graphs is to recover underlying labels/attributes of users (e.g., political affiliation) given the connectivity between users (represented by adjacency matrix of a graph). There has been significant recent progress on understanding the fundamental limits of community detection when the graph is generated from a stochastic block model (SBM). Specifically, sharp information theoretic limits and efficient algorithms have been obtained for SBMs as a function of p and q, which represent the intra-community and inter-community connection probabilities. In this paper, we study the community detection problem while preserving the privacy of the individual connections (edges) between the vertices. Focusing on the notion of ( , δ)-edge differential privacy (DP), we seek to understand the fundamental tradeoffs between (p, q), DP budget ( , δ), and computational efficiency for exact recovery of the community labels.To this end, we present and analyze the associated information-theoretic tradeoffs for three broad classes of differentially private community recovery mechanisms: a) stability based mechanism; b) sampling based mechanisms; and c) graph perturbation mechanisms. Our main findings are that stability and sampling based mechanisms lead to a superior tradeoff between (p, q) and the privacy budget ( , δ); however this comes at the expense of higher computational complexity. On the other hand, albeit low complexity, graph perturbation mechanisms require the privacy budget to scale as Ω(log(n)) for exact recovery. To the best of our knowledge, this is the first work to study the impact of privacy constraints on the fundamental limits for community detection.

show abstract

Section: Related Workmentioning

confidence: 99%

Differentially Private Community Detection for Stochastic Block Models

Seif¹,

Nguyen²,

Vullikanti³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Due to the difficulty in obtaining high utility private mechanisms, there is less number of graph statistics made private in the node differential privacy framework. That said, some recent works studied private estimation of generative graph model parameters [13,14,123], such as the edge probability in the Erdős-Rényi model. Sometimes, instead of a static graph, there may be a sequence of dynamic graphs.…”

Section: Node Differential Privacymentioning

confidence: 99%

“…Community Detection [97], Edge Weight [25,81] Egocentric Betweenness Centrality [114] Subgraph Counting: [23,63,84,99,107,152] Degree Sequence: [47,64,106] Cut Query: [10,43,137] Node DP Erdős-Rényi Model Parameter [13,14,123],…”

Section: Introductionmentioning

confidence: 99%

Private Graph Data Release: A Survey

Yang¹,

Purcell²,

Rakotoarivelo³

et al. 2021

Preprint

View full text Add to dashboard Cite

The application of graph analytics to various domains have yielded tremendous societal and economical benefits in recent years. However, the increasingly widespread adoption of graph analytics comes with a commensurate increase in the need to protect private information in graph databases, especially in light of the many privacy breaches in real-world graph data that was supposed to preserve sensitive information. This paper provides a comprehensive survey of private graph data release algorithms that seek to achieve the fine balance between privacy and utility, with a specific focus on provably private mechanisms. Many of these mechanisms fall under natural extensions of the Differential Privacy framework to graph data, but we also investigate more general privacy formulations like Pufferfish Privacy that can deal with the limitations of Differential Privacy. A wide-ranging survey of the applications of private graph data release mechanisms to social networks, finance, supply chain, health and energy is also provided. This survey paper and the taxonomy it provides should benefit practitioners and researchers alike in the increasingly important area of private graph data release and analysis.

show abstract

“…When it comes to privacy preserving, it is necessary to bound all possible α M (λ; D, D ′ ), denoted as α M (λ), which is defined as: By the combination of ( 34) and (35), without loss of generality:…”

Section: A Details Of Proof A1 Theoremmentioning

confidence: 99%

“…It preserves sensitive information by adding random noise, making an adversary can not infer any single data instance in the dataset by observing model parameters. Differential privacy has received a great deal of attentions and has been applied to regression [10], [38], [6], boosting [20], [50], PCA [12], [42], GAN [45], [47], transfer learning [31], graph algorithms [35], [39], [3], deep learning [36], [1] and other fields.…”

Section: Introductionmentioning

confidence: 99%

Input Perturbation: A New Paradigm between Central and Local Differential Privacy

Kang,

Liu,

Niu

et al. 2020

Preprint

View full text Add to dashboard Cite

Traditionally, there are two models on differential privacy: the central model and the local model. The central model focuses on the machine learning model and the local model focuses on the training data. In this paper, we study the input perturbation method in differentially private empirical risk minimization (DP-ERM), preserving privacy of the central model. By adding noise to the original training data and training with the 'perturbed data', we achieve (ϵ,δ )-differential privacy on the final model, along with some kind of privacy on the original data. We observe that there is an interesting connection between the local model and the central model: the perturbation on the original data causes the perturbation on the gradient, and finally the model parameters. This observation means that our method builds a bridge between local and central model, protecting the data, the gradient and the model simultaneously, which is more superior than previous central methods. Detailed theoretical analysis and experiments show that our method achieves almost the same (or even better) performance as some of the best previous central methods with more protections on privacy, which is an attractive result. Moreover, we extend our method to a more general case: the loss function satisfies the Polyak-Lojasiewicz condition, which is more general than strong convexity, the constraint on the loss function in most previous work.

show abstract

Efficiently Estimating Erdos-Renyi Graphs with Node Differential Privacy

Cited by 4 publications

References 4 publications

Differentially Private Community Detection for Stochastic Block Models

Differentially Private Community Detection for Stochastic Block Models

Private Graph Data Release: A Survey

Input Perturbation: A New Paradigm between Central and Local Differential Privacy

Contact Info

Product

Resources

About