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Differentially Private Estimation of Principal Components and Covariance

Published on:

8 January 2024

Primary Category:

Statistics Theory

Paper Authors:

T. Tony Cai,

Dong Xia,

Mengyue Zha

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Key Details

Establishes minimax rates for private PCA and covariance estimation

Allows rank to grow and removes eigengap conditions

Introduces computationally efficient private estimators

Proves optimality of proposed estimators

Derives matching minimax lower bounds

AI generated summary

Differentially Private Estimation of Principal Components and Covariance

This paper studies optimal algorithms for differentially private estimation of principal components and covariance matrices. The authors establish minimax optimal rates of convergence, allowing the rank to grow with dimension and removing eigengap conditions. Efficient differentially private estimators are introduced and proven to achieve the optimal rates. Matching information-theoretic lower bounds are also derived.

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