Differentially private high dimensional sparse covariance matrix estimation
KAUST DepartmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
Online Publication Date2021-03-11
Print Publication Date2021-03
Embargo End Date2023-03-10
Permanent link to this recordhttp://hdl.handle.net/10754/668232
MetadataShow full item record
AbstractIn this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to achieve a non-trivial ℓ2-norm based error bound whose dependence on the dimension drops to logarithmic instead of polynomial, it is significantly better than the existing ones, which add noise directly to the empirical covariance matrix. We also extend the ℓ2-norm based error bound to a general ℓw-norm based one for any 1≤w≤∞, and show that they share the same upper bound asymptotically. Our approach can be easily extended to local differential privacy. Experiments on the synthetic datasets show results that are consistent with theoretical claims.
CitationWang, D., & Xu, J. (2021). Differentially private high dimensional sparse covariance matrix estimation. Theoretical Computer Science. doi:10.1016/j.tcs.2021.03.001
SponsorsThis research was supported in part by the National Science Foundation (NSF) through grants CCF-1422324 and CCF-1716400.
JournalTheoretical Computer Science