mlsanityData to 7 Oct 2026

Matrix Factorization for Practical Continual Mean Estimation Under User-Level Differential Privacy

arXiv 2601.22320 ↗First posted 29 Jan 2026cs.LG stat.MLcited by 0

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Abstract (arXiv)

We study continual mean estimation, where data vectors arrive sequentially and the goal is to maintain accurate estimates of the running mean. We address this problem under user-level differential privacy, which protects each user's entire dataset even when they contribute multiple data points. Previous work on this problem has focused on pure differential privacy. While important, this approach limits applicability, as it leads to overly noisy estimates. In contrast, we analyze the problem under approximate differential privacy, adopting recent advances in the Matrix Factorization mechanism. We introduce a novel mean estimation specific factorization, which is both efficient and accurate, achieving asymptotically lower mean-squared error bounds in continual mean estimation under user-level differential privacy.

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References · 36

  1. 2023How to DP-fy ML: A Practical Guide to Machine Learning with Differential Privacycited by 150
  2. 2017Finite Sample Differentially Private Confidence Intervalscited by 103
  3. 2020Private Mean Estimation of Heavy-Tailed Distributionscited by 73
  4. 2021Learning with User-Level Privacycited by 72
  5. 2022Improved Differential Privacy for SGD via Optimal Private Linear Operators on Adaptive Streamscited by 59
  6. 2023(Amplified) Banded Matrix Factorization: A unified approach to private trainingcited by 49
  7. 2022Multi-Epoch Matrix Factorization Mechanisms for Private Machine Learningcited by 48
  8. 2020Learning discrete distributions: user vs item-level privacycited by 41
  9. 2020Encode, Shuffle, Analyze Privacy Revisited: Formalizations and Empirical Evaluationcited by 39
  10. 2019The Power of Factorization Mechanisms in Local and Central Differential Privacycited by 30
  11. 2021Tight and Robust Private Mean Estimation with Few Userscited by 26
  12. 2022Constant matters: Fine-grained Complexity of Differentially Private Continual Observationcited by 23
24 more
  1. 2023Correlated Noise Provably Beats Independent Noise for Differentially Private Learningcited by 23
  2. 2024Mind the Privacy Unit! User-Level Differential Privacy for Language Model Fine-Tuningcited by 21
  3. 2022Discrete Distribution Estimation under User-level Local Differential Privacycited by 17
  4. 2023Federated Linear Contextual Bandits with User-level Differential Privacycited by 12
  5. 2023A Smooth Binary Mechanism for Efficient Private Continual Observationcited by 12
  6. 2023User-Level Differential Privacy With Few Examples Per Usercited by 12
  7. 2023User-level Differentially Private Stochastic Convex Optimization: Efficient Algorithms with Optimal Ratescited by 12
  8. 2024Banded Square Root Matrix Factorization for Differentially Private Model Trainingcited by 12
  9. 2024Scaling up the Banded Matrix Factorization Mechanism for Differentially Private MLcited by 12
  10. 2024Lower Bounds for Differential Privacy Under Continual Observation and Online Threshold Queriescited by 11
  11. 2023ULDP-FL: Federated Learning with Across Silo User-Level Differential Privacycited by 9
  12. 2023Mean Estimation with User-level Privacy under Data Heterogeneitycited by 8
  13. 2025Back to Square Roots: An Optimal Bound on the Matrix Factorization Error for Multi-Epoch Differentially Private SGDcited by 7
  14. 2024Private Mean Estimation with Person-Level Differential Privacycited by 6
  15. 2022Continual Mean Estimation Under User-Level Privacycited by 5
  16. 2025Continual Release Moment Estimation with Differential Privacycited by 5
  17. 2024Improved Communication-Privacy Trade-offs in L2 Mean Estimation under Streaming Differential Privacycited by 4
  18. 2024Count on Your Elders: Laplace vs Gaussian Noisecited by 4
  19. 2024Faster Algorithms for User-Level Private Stochastic Convex Optimizationcited by 4
  20. 2024Learning with User-Level Local Differential Privacycited by 3
  21. 2025Normalized Square Root: Sharper Matrix Factorization Bounds for Differentially Private Continual Countingcited by 3
  22. 2025Private Continual Counting of Unbounded Streamscited by 2
  23. 2024Distribution-Aware Mean Estimation under User-level Local Differential Privacycited by 1
  24. 2025Privacy for Free: Leveraging Local Differential Privacy Perturbed Data from Multiple Servicescited by 1

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