Minimax and Adaptive Covariance Matrix Estimation under Differential Privacy

arXiv:2603.19703 · math.ST, cs.LG, stat.TH · Submitted 2026-03-20 · Read on arXiv

math.ST, cs.LG, stat.TH

Submitted: 2026-03-20

Updated: 2026-09-25

Terminology

• Differential Privacy — 58× in this paper · explained in 4 episodes
• Fisher Information — 31× in this paper · explained in 3 episodes
• Adaptation — 18× in this paper · explained in 1 episode
• Differentially Private — 13× in this paper · explained in 3 episodes
• Trace — 12× in this paper · explained in 2 episodes
• Aggregation — 9× in this paper · explained in 1 episode
• alpha — 7× in this paper · explained in 1 episode
• Benchmark — 6× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Ambient Dimension — 4× in this paper · explained in 1 episode
• Fingerprinting — 4× in this paper · explained in 2 episodes
• Score Function — 4× in this paper · explained in 4 episodes
• Loss Function — 3× in this paper · explained in 2 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Sparsity — 3× in this paper · explained in 4 episodes
• Regret — 2× in this paper · explained in 3 episodes
• Adaptive Selection — 1× in this paper · explained in 1 episode
• Admissibility — 1× in this paper · explained in 2 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Differential Privacy (DP) — 1× in this paper · explained in 7 episodes
• Error Decomposition — 1× in this paper · explained in 3 episodes
• Federated Learning — 1× in this paper · explained in 14 episodes
• Longitudinal Data — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning
• Optimal Differentially Private PCA and Estimation for Spiked Covariance Matrices
• Optimal estimation in private distributed functional data analysis

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