# Robust Estimation of Sparse Numerical Vectors under Local Differential Privacy

arXiv: https://arxiv.org/abs/2607.27815 · HTML: https://mlsanity.com/paper/2607.27815/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 58 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Differentially Private Learning with Adaptive Clipping](https://mlsanity.com/paper/1905.03871/) (2019)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Understanding Clipping for Federated Learning: Convergence and Client-Level Differential Privacy](https://mlsanity.com/paper/2106.13673/) (2021)
- [Breaking the Communication-Privacy-Accuracy Trilemma](https://mlsanity.com/paper/2007.11707/) (2020)
- [Collecting and Analyzing Multidimensional Data with Local Differential Privacy](https://mlsanity.com/paper/1907.00782/) (2019)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [Optimal Schemes for Discrete Distribution Estimation under Locally Differential Privacy](https://mlsanity.com/paper/1702.00610/) (2017)
- [Stronger Privacy Amplification by Shuffling for R'enyi and Approximate Differential Privacy](https://mlsanity.com/paper/2208.04591/) (2022)
- [Manipulation Attacks in Local Differential Privacy](https://mlsanity.com/paper/1909.09630/) (2019)
- [Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication](https://mlsanity.com/paper/1802.04705/) (2018)
- [Data Poisoning Attacks to Local Differential Privacy Protocols](https://mlsanity.com/paper/1911.02046/) (2019)
- [Collecting and Analyzing Data from Smart Device Users with Local Differential Privacy](https://mlsanity.com/paper/1606.05053/) (2016)
- [Estimating Numerical Distributions under Local Differential Privacy](https://mlsanity.com/paper/1912.01051/) (2019)
- [Fast Optimal Locally Private Mean Estimation via Random Projections](https://mlsanity.com/paper/2306.04444/) (2023)
- [Lightweight Techniques for Private Heavy Hitters](https://mlsanity.com/paper/2012.14884/) (2020)
- [Locally Differentially Private Frequency Estimation with Consistency](https://mlsanity.com/paper/1905.08320/) (2019)
- [Poisoning Attacks to Local Differential Privacy Protocols for Key-Value Data](https://mlsanity.com/paper/2111.11534/) (2021)
- [Fine-grained Poisoning Attack to Local Differential Privacy Protocols for Mean and Variance Estimation](https://mlsanity.com/paper/2205.11782/) (2022)
- [PCKV: Locally Differentially Private Correlated Key-Value Data Collection with Optimized Utility](https://mlsanity.com/paper/1911.12834/) (2019)
- [On the Robustness of LDP Protocols for Numerical Attributes under Data Poisoning Attacks](https://mlsanity.com/paper/2403.19510/) (2024)
- [Data Poisoning Attacks to Locally Differentially Private Frequent Itemset Mining Protocols](https://mlsanity.com/paper/2406.19466/) (2024)
- [Calibrate: Frequency Estimation and Heavy Hitter Identification with Local Differential Privacy via Incorporating Prior Knowledge](https://mlsanity.com/paper/1812.02055/) (2018)
- [Differentially Private Numerical Vector Analyses in the Local and Shuffle Model](https://mlsanity.com/paper/2304.04410/) (2023)
- [Almost Instance-optimal Clipping for Summation Problems in the Shuffle Model of Differential Privacy](https://mlsanity.com/paper/2403.10116/) (2024)
- [Consistent Estimation of Numerical Distributions under Local Differential Privacy by Wavelet Expansion](https://mlsanity.com/paper/2509.19661/) (2025)

## Abstract (arXiv)

Local differential privacy (LDP) protocols are vulnerable to poisoning attacks. Existing research have proposed efficient defense strategies for single-item users. However, in practice, a user may possess multiple items. The defense against poisoning attacks for multi-item users is challenging, because due to larger output spaces, the adversary can conduct more powerful attacks without being detected. In this paper, we address the robust sparse vector mean estimation problem, in which each user has a vector with m nonzero coordinates. We propose Randomized Projection with Clipping (RPC). Firstly, the server sends a random binary vector to each user. The user then projects its local data on the vector, and clip the value to restrict the attacker's capability. To handle clipping bias, we propose a correction method based on a careful analysis that gives an exact expression of the bias. As a result, bias-variance tradeoff is no longer needed, thus the clipping threshold can be further reduced to shrink the output space and enhance robustness. We provide a rigorous theoretical guarantee of the estimation error under all possible attacks. Numerical experiments show that under trusted environments, our new method achieves comparable or better performance than existing methods, indicating that our method is already an efficient estimator in its own right. Under untrusted environments, our method is also significantly more robust to poisoning attacks.