8 January 2024
T. Tony Cai,
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
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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