mlsanityData to 7 Oct 2026

Robust Testing and Estimation under Manipulation Attacks

arXiv 2104.10740 ↗First posted 21 Apr 2021cs.IT cs.DM cs.LGcited by 5

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Abstract (arXiv)

We study robust testing and estimation of discrete distributions in the strong contamination model. We consider both the "centralized setting" and the "distributed setting with information constraints" including communication and local privacy (LDP) constraints. Our technique relates the strength of manipulation attacks to the earth-mover distance using Hamming distance as the metric between messages(samples) from the users. In the centralized setting, we provide optimal error bounds for both learning and testing. Our lower bounds under local information constraints build on the recent lower bound methods in distributed inference. In the communication constrained setting, we develop novel algorithms based on random hashing and an ℓ1/ℓ1 isometry.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 24 of its 36 references that are in the map. First posted on arXiv 21 Apr 2021.

Builds on

24 of 36 references.

References · 24

  1. 2019Advances and Open Problems in Federated Learningcited by 3,021
  2. 2018How To Backdoor Federated Learningcited by 745
  3. 2018Analyzing Federated Learning through an Adversarial Lenscited by 346
  4. 2016Robust Estimators in High Dimensions without the Computational Intractabilitycited by 209
  5. 2016Agnostic Estimation of Mean and Covariancecited by 131
  6. 2019Recent Advances in Algorithmic High-Dimensional Robust Statisticscited by 100
  7. 2016Discrete Distribution Estimation under Local Privacycited by 58
  8. 2013Optimal Algorithms for Testing Closeness of Discrete Distributionscited by 37
  9. 2015Differentially Private Ordinary Least Squarescited by 36
  10. 2018Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraintscited by 33
  11. 2018Inference under Information Constraints I: Lower Bounds from Chi-Square Contractioncited by 31
  12. 2017Differentially Private Testing of Identity and Closeness of Discrete Distributionscited by 25
12 more
  1. 2019Manipulation Attacks in Local Differential Privacycited by 23
  2. 2019Inference under Information Constraints II: Communication Constraints and Shared Randomnesscited by 22
  3. 2017Optimal Identity Testing with High Probabilitycited by 19
  4. 2020Interactive Inference under Information Constraintscited by 15
  5. 2017Which Distribution Distances are Sublinearly Testable?cited by 14
  6. 2017Learning Discrete Distributions from Untrusted Batchescited by 14
  7. 2018Test without Trust: Optimal Locally Private Distribution Testingcited by 13
  8. 2019Optimal Robust Learning of Discrete Distributions from Batchescited by 10
  9. 2020Learning Structured Distributions From Untrusted Batches: Faster and Simplercited by 8
  10. 2020A General Method for Robust Learning from Batchescited by 8
  11. 2019Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fitcited by 5
  12. 2020The Sample Complexity of Robust Covariance Testingcited by 5

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 1; 2025: 1.

5 papers.

  1. 2023On the Privacy-Robustness-Utility Trilemma in Distributed Learningcited by 24
  2. 2025Towards Trustworthy Federated Learning with Untrusted Participantscited by 8
  3. 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7
  4. 2022Robust Estimation of Discrete Distributions under Local Differential Privacycited by 5
  5. 2023Balancing Privacy, Robustness, and Efficiency in Machine Learningcited by 1