# On the Risks of Collecting Multidimensional Data Under Local Differential Privacy

arXiv: https://arxiv.org/abs/2209.01684 · HTML: https://mlsanity.com/paper/2209.01684/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2022.

## Built on by (most cited first, 3 of 3)

- [Understanding Disclosure Risk in Differential Privacy with Applications to Noise Calibration and Auditing (Extended Version)](https://mlsanity.com/paper/2603.12142/) (2026)
- [On the Utility Gain of Iterative Bayesian Update for Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2307.07744/) (2023)
- [Training Set Reconstruction from Differentially Private Forests: How Effective is DP?](https://mlsanity.com/paper/2502.05307/) (2025)

## Abstract (arXiv)

The private collection of multiple statistics from a population is a fundamental statistical problem. One possible approach to realize this is to rely on the local model of differential privacy (LDP). Numerous LDP protocols have been developed for the task of frequency estimation of single and multiple attributes. These studies mainly focused on improving the utility of the algorithms to ensure the server performs the estimations accurately. In this paper, we investigate privacy threats (re-identification and attribute inference attacks) against LDP protocols for multidimensional data following two state-of-the-art solutions for frequency estimation of multiple attributes. To broaden the scope of our study, we have also experimentally assessed five widely used LDP protocols, namely, generalized randomized response, optimal local hashing, subset selection, RAPPOR and optimal unary encoding. Finally, we also proposed a countermeasure that improves both utility and robustness against the identified threats. Our contributions can help practitioners aiming to collect users' statistics privately to decide which LDP mechanism best fits their needs.