Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacy

arXiv:2609.26508 · cs.LG, cs.DS, stat.ML · Submitted 2026-09-22 · Read on arXiv

cs.LG, cs.DS, stat.ML

Submitted: 2026-09-22

Updated: 2026-09-22

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Sample Complexity — 16× in this paper · explained in 15 episodes
• Trace — 12× in this paper · explained in 2 episodes
• Differentially Private — 11× in this paper · explained in 3 episodes
• Differential Privacy — 9× in this paper · explained in 4 episodes
• Aggregation — 7× in this paper · explained in 1 episode
• Principal Component Analysis (PCA) — 3× in this paper · explained in 4 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Sample Complexity Scaling — 2× in this paper · explained in 2 episodes
• Uncertainty Quantification — 2× in this paper · explained in 8 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Analyzer — 1× in this paper · explained in 1 episode

Sources

• Optimal Differentially Private PCA and Estimation for Spiked Covariance Matrices
• Fast and Simple PCA via Convex Optimization

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