Abstract
Many machine learning problems, such as medical data summarization and social welfare maximization, can be modeled as the problems of maximizing monotone submodular functions. Differentially private submodular functions under cardinality constraints are first proposed and studied to solve the Combinatorial Public Projects (CPP) problem, in order to protect personal data privacy while processing sensitive data. However, the research of these functions for privacy protection has received little attention so far. In this paper, we propose to study the differentially private submodular maximization problem over the integer lattice. Our main contributions are to present differentially private approximation algorithms for both DR-submodular and integer submodular function maximization problems under cardinality constraints and analyze the sensitivity of our algorithms.
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Acknowledgements
The first two authors are supported by National Natural Science Foundation of China (No. 12131003) and Beijing Natural Science Foundation Project No. Z200002. The third author is supported by National Natural Sciences and Engineering Research Council of Canada (NSERC) grant 06446, and National Natural Science Foundation of China (Nos. 11771386, 11728104). The fourth author is supported by the Province Natural Science Foundation of Shandong (No. ZR2017MA031) and the National Natural Science Foundation of China (No. 11801310).
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Hu, J., Xu, D., Du, D., Miao, C. (2021). Differentially Private Submodular Maximization over Integer Lattice. In: Mohaisen, D., Jin, R. (eds) Computational Data and Social Networks. CSoNet 2021. Lecture Notes in Computer Science(), vol 13116. Springer, Cham. https://doi.org/10.1007/978-3-030-91434-9_6
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