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Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes
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We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the Stein-Haff identity, an extension of the classical Stein's identity used in previous fingerprinting lemma arguments.
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Cited by 2 Pith papers
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Fingerprinting Codes Meet Geometry: Improved Lower Bounds for Private Query Release and Adaptive Data Analysis
The geometric fingerprinting framework yields new lower bounds for adaptive data analysis and random queries, but the claimed log(1/delta) matching bound for private query release is not established by the proof.
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Lower Bounds for Public-Private Learning under Distribution Shift
For Gaussian mean estimation and linear regression with distribution shift, the paper claims that public data never provides complementary value: either public data alone suffices, or (for large shifts) private data a...
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