# Robust Testing and Estimation under Manipulation Attacks

arXiv: https://arxiv.org/abs/2104.10740 · HTML: https://mlsanity.com/paper/2104.10740/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 21 Apr 2021.

## Builds on (most cited first, 24 of 24)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [How To Backdoor Federated Learning](https://mlsanity.com/paper/1807.00459/) (2018)
- [Analyzing Federated Learning through an Adversarial Lens](https://mlsanity.com/paper/1811.12470/) (2018)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Agnostic Estimation of Mean and Covariance](https://mlsanity.com/paper/1604.06968/) (2016)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [Discrete Distribution Estimation under Local Privacy](https://mlsanity.com/paper/1602.07387/) (2016)
- [Optimal Algorithms for Testing Closeness of Discrete Distributions](https://mlsanity.com/paper/1308.3946/) (2013)
- [Differentially Private Ordinary Least Squares](https://mlsanity.com/paper/1507.02482/) (2015)
- [Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints](https://mlsanity.com/paper/1802.08417/) (2018)
- [Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction](https://mlsanity.com/paper/1812.11476/) (2018)
- [Manipulation Attacks in Local Differential Privacy](https://mlsanity.com/paper/1909.09630/) (2019)
- [Differentially Private Testing of Identity and Closeness of Discrete Distributions](https://mlsanity.com/paper/1707.05128/) (2017)
- [Inference under Information Constraints II: Communication Constraints and Shared Randomness](https://mlsanity.com/paper/1905.08302/) (2019)
- [Optimal Identity Testing with High Probability](https://mlsanity.com/paper/1708.02728/) (2017)
- [Interactive Inference under Information Constraints](https://mlsanity.com/paper/2007.10976/) (2020)
- [Which Distribution Distances are Sublinearly Testable?](https://mlsanity.com/paper/1708.00002/) (2017)
- [Learning Discrete Distributions from Untrusted Batches](https://mlsanity.com/paper/1711.08113/) (2017)
- [Test without Trust: Optimal Locally Private Distribution Testing](https://mlsanity.com/paper/1808.02174/) (2018)
- [Optimal Robust Learning of Discrete Distributions from Batches](https://mlsanity.com/paper/1911.08532/) (2019)
- [Learning Structured Distributions From Untrusted Batches: Faster and Simpler](https://mlsanity.com/paper/2002.10435/) (2020)
- [A General Method for Robust Learning from Batches](https://mlsanity.com/paper/2002.11099/) (2020)
- [Domain Compression and its Application to Randomness-Optimal Distributed Goodness-of-Fit](https://mlsanity.com/paper/1907.08743/) (2019)
- [The Sample Complexity of Robust Covariance Testing](https://mlsanity.com/paper/2012.15802/) (2020)

## Built on by (most cited first, 5 of 5)

- [On the Privacy-Robustness-Utility Trilemma in Distributed Learning](https://mlsanity.com/paper/2302.04787/) (2023)
- [Towards Trustworthy Federated Learning with Untrusted Participants](https://mlsanity.com/paper/2505.01874/) (2025)
- [Robust Kernel Hypothesis Testing under Data Corruption](https://mlsanity.com/paper/2405.19912/) (2024)
- [Robust Estimation of Discrete Distributions under Local Differential Privacy](https://mlsanity.com/paper/2202.06825/) (2022)
- [Balancing Privacy, Robustness, and Efficiency in Machine Learning](https://mlsanity.com/paper/2312.14712/) (2023)

## 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.