---
title: "Hiding Numerical Vectors in Local Private and Shuffled Messages"
authors:
  - "Shaowei Wang"
  - "Jin Li"
  - "Yuqiu Qian"
  - "Jiachun Du"
  - "Wenqing Lin"
  - "Wei Yang"
doi: "10.24963/ijcai.2021/510"
url: "https://ijcai.org/proceedings/2021/510"
pdf: "https://ijcai.org/proceedings/2021/0510.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "3706-3712"
track: "Main Track"
keywords:
  - "Multidisciplinary Topics and Applications: Security and Privacy"
---

# Hiding Numerical Vectors in Local Private and Shuffled Messages

Shaowei Wang, Jin Li, Yuqiu Qian, Jiachun Du, Wenqing Lin, Wei Yang

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 3706-3712. DOI: [10.24963/ijcai.2021/510](https://doi.org/10.24963/ijcai.2021/510)

## Abstract

Numerical vector aggregation has numerous applications in privacy-sensitive scenarios, such as distributed gradient estimation in federated learning, and statistical analysis on key-value data. Within the framework of local differential privacy, this work gives tight minimax error bounds of O(d s/(n epsilon^2)), where d is the dimension of the numerical vector and s is the number of non-zero entries. An attainable mechanism is then designed to improve from existing approaches suffering error rate of O(d^2/(n epsilon^2)) or O(d s^2/(n epsilon^2)). To break the error barrier in the local privacy, this work further consider privacy amplification in the shuffle model with anonymous channels, and shows the mechanism satisfies centralized (14 ln(2/delta) (s e^epsilon+2s-1)/(n-1))^0.5, delta)-differential privacy, which is domain independent and thus scales to federated learning of large models. We experimentally validate and compare it with existing approaches,  and demonstrate its significant error reduction.