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dc.contributor.authorWang, Di
dc.contributor.authorXu, Jinhui
dc.date.accessioned2020-12-14T08:40:57Z
dc.date.available2020-12-14T08:40:57Z
dc.date.issued2020-11-25
dc.date.submitted2005-04-19
dc.identifier.citationWang, D., & Xu, J. (2020). On Sparse Linear Regression in the Local Differential Privacy Model. IEEE Transactions on Information Theory, 1–1. doi:10.1109/tit.2020.3040406
dc.identifier.issn1557-9654
dc.identifier.issn0018-9448
dc.identifier.doi10.1109/TIT.2020.3040406
dc.identifier.urihttp://hdl.handle.net/10754/666352
dc.description.abstractIn this paper, we study the sparse linear regression problem under the Local Differential Privacy (LDP) model. We first show that polynomial dependency on the dimensionality p of the space is unavoidable for the estimation error in both non-interactive and sequential interactive local models, if the privacy of the whole dataset needs to be preserved. Similar limitations also exist for other types of error measurements and in the relaxed local models. This indicates that differential privacy in high dimensional space is unlikely achievable for the problem. With the understanding of this limitation, we then present two algorithmic results. The first one is a sequential interactive LDP algorithm for the low dimensional sparse case, called Locally Differentially Private Iterative Hard Thresholding (LDP-IHT), which achieves a near optimal upper bound. This algorithm is actually rather general and can be used to solve quite a few other problems, such as (Local) DP-ERM with sparsity constraints and sparse regression with non-linear measurements. The second one is for the restricted (high dimensional) case where only the privacy of the responses (labels) needs to be preserved. For this case, we show that the optimal rate of the error estimation can be made logarithmically dependent on p (i.e., log p) in the local model, where an upper bound is obtained by a label-privacy version of LDP-IHT. Experiments on real world and synthetic datasets confirm our theoretical analysis.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.urlhttps://ieeexplore.ieee.org/document/9269994/
dc.rights(c) 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
dc.titleOn Sparse Linear Regression in the Local Differential Privacy Model
dc.typeArticle
dc.contributor.departmentDivision of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.
dc.identifier.journalIEEE Transactions on Information Theory
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY, 14260 USA.
dc.identifier.pages1-1
kaust.personWang, Di
dc.date.accepted2015-08-26
dc.identifier.eid2-s2.0-85097176069
dc.date.published-online2020-11-25
dc.date.published-print2021-02


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