Differentially Private Covariance Revisited

05/28/2022

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by   Wei Dong, et al.

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In this paper, we present three new error bounds, in terms of the Frobenius norm, for covariance estimation under differential privacy: (1) a worst-case bound of Õ(d^1/4/√(n)), which improves the standard Gaussian mechanism Õ(d/n) for the regime d>Ω(n^2/3); (2) a trace-sensitive bound that improves the state of the art by a √(d)-factor, and (3) a tail-sensitive bound that gives a more instance-specific result. The corresponding algorithms are also simple and efficient. Experimental results show that they offer significant improvements over prior work.