Lower Bound of Locally Differentially Private Sparse Covariance Matrix Estimation
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In this paper, we study the sparse covariance matrix estimation problem in the local differential privacy model, and give a non-trivial lower bound on the non-interactive private minimax risk in the metric of squared spectral norm. We show that the lower bound is actually tight, as it matches a previous upper bound. Our main technique for achieving this lower bound is a general framework, called General Private Assouad Lemma, which is a considerable generalization of the previous private Assouad lemma and can be used as a general method for bounding the private minimax risk of matrix-related estimation problems.
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2019 ◽
Vol 67
(10)
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pp. 2707-2719
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2010 ◽
Vol 46
(1)
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pp. 375-396
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2014 ◽
Vol 3
(2)
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pp. 231-250
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2011 ◽
Vol 106
(494)
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pp. 672-684
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