Journal
JOURNAL OF MACHINE LEARNING RESEARCH
Volume 23, Issue -, Pages -Publisher
MICROTOME PUBL
Keywords
Asymptotic normality; Consistency; Differential privacy; Synthetic graph; Two-mode network
Funding
- National Natural Science Foundation of China [NSFC 12001459]
- Hong Kong Research Grants Council Gerneral Research Fund [GRF15302722]
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This paper introduces the characteristics and privacy risks of two-mode network data, and proposes a weak notion of edge differential privacy for releasing the degree sequence of these networks. The consistency and asymptotic normality of two differential privacy estimators are established, and an efficient algorithm for generating synthetic bipartite graphs is developed. Numerical simulations and real data applications verify the usefulness of the proposed method.
Many network data encountered are two-mode networks. These networks are characterized by having two sets of nodes and links are only made between nodes belonging to different sets. While their two-mode feature triggers interesting interactions, it also increases the risk of privacy exposure, and it is essential to protect sensitive information from being disclosed when releasing these data. In this paper, we introduce a weak notion of edge differential privacy and propose to release the degree sequence of a two-mode network by adding non-negative Laplacian noises that satisfies this privacy definition. Under mild conditions for an exponential-family model for bipartite graphs in which each node is individually parameterized, we establish the consistency and asymptotic normality of two differential privacy estimators, the first based on moment equations and the second after denoising the noisy sequence. For the latter, we develop an efficient algorithm which produces a readily useful synthetic bipartite graph. Numerical simulations and a real data application are carried out to verify our theoretical results and demonstrate the usefulness of our proposal.
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