# Collecting and Analyzing Multidimensional Data with Local Differential Privacy

arXiv: https://arxiv.org/abs/1907.00782 · HTML: https://mlsanity.com/paper/1907.00782/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2019.

## Built on by (most cited first, 30 of 49)

- [Stronger Privacy for Federated Collaborative Filtering with Implicit Feedback](https://mlsanity.com/paper/2105.03941/) (2021)
- [Active Membership Inference Attack under Local Differential Privacy in Federated Learning](https://mlsanity.com/paper/2302.12685/) (2023)
- [Transparent Contribution Evaluation for Secure Federated Learning on Blockchain](https://mlsanity.com/paper/2101.10572/) (2021)
- [OpBoost: A Vertical Federated Tree Boosting Framework Based on Order-Preserving Desensitization](https://mlsanity.com/paper/2210.01318/) (2022)
- [XRand: Differentially Private Defense against Explanation-Guided Attacks](https://mlsanity.com/paper/2212.04454/) (2022)
- [Residue-based Label Protection Mechanisms in Vertical Logistic Regression](https://mlsanity.com/paper/2205.04166/) (2022)
- [FedXGBoost: Privacy-Preserving XGBoost for Federated Learning](https://mlsanity.com/paper/2106.10662/) (2021)
- [Fine-grained Poisoning Attack to Local Differential Privacy Protocols for Mean and Variance Estimation](https://mlsanity.com/paper/2205.11782/) (2022)
- [FLSys: Toward an Open Ecosystem for Federated Learning Mobile Apps](https://mlsanity.com/paper/2111.09445/) (2021)
- [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022)
- [Blink: Link Local Differential Privacy in Graph Neural Networks via Bayesian Estimation](https://mlsanity.com/paper/2309.03190/) (2023)
- [Task-aware Privacy Preservation for Multi-dimensional Data](https://mlsanity.com/paper/2110.02329/) (2021)
- [(Local) Differential Privacy has NO Disparate Impact on Fairness](https://mlsanity.com/paper/2304.12845/) (2023)
- [FedGES: A Federated Learning Approach for BN Structure Learning](https://mlsanity.com/paper/2502.01538/) (2025)
- [Multi-Party Dual Learning](https://mlsanity.com/paper/2104.06677/) (2021)
- [FedPerm: Private and Robust Federated Learning by Parameter Permutation](https://mlsanity.com/paper/2208.07922/) (2022)
- [Towards Differential Privacy in Sequential Recommendation: A Noisy Graph Neural Network Approach](https://mlsanity.com/paper/2309.11515/) (2023)
- [Privacy-Preserving Graph Embedding based on Local Differential Privacy](https://mlsanity.com/paper/2310.11060/) (2023)
- [Heterogeneous Randomized Response for Differential Privacy in Graph Neural Networks](https://mlsanity.com/paper/2211.05766/) (2022)
- [Privacy-preserving Federated Primal-dual Learning for Non-convex and Non-smooth Problems with Model Sparsification](https://mlsanity.com/paper/2310.19558/) (2023)
- [How Much is Left? LLMs Linearly Encode Their Remaining Output Length](https://mlsanity.com/paper/2607.05316/) (2026)
- [WebFed: Cross-platform Federated Learning Framework Based on Web Browser with Local Differential Privacy](https://mlsanity.com/paper/2110.11646/) (2021)
- [Locally Differentially Private Bayesian Inference](https://mlsanity.com/paper/2110.14426/) (2021)
- [Locally Differentially Private Distributed Deep Learning via Knowledge Distillation](https://mlsanity.com/paper/2202.02971/) (2022)
- [One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation](https://mlsanity.com/paper/2202.07194/) (2022)
- [Enabling Trade-offs in Privacy and Utility in Genomic Data Beacons and Summary Statistics](https://mlsanity.com/paper/2302.01763/) (2023)
- [Shuffled Differentially Private Federated Learning for Time Series Data Analytics](https://mlsanity.com/paper/2307.16196/) (2023)
- [Scalable and Privacy-Preserving Synthetic Data Generation on Decentralised Web](https://mlsanity.com/paper/2310.20062/) (2023)
- [Privacy-Preserving Heterogeneous Federated Learning for Sensitive Healthcare Data](https://mlsanity.com/paper/2406.10563/) (2024)
- [Beyond Statistical Estimation: Differentially Private Individual Computation via Shuffling](https://mlsanity.com/paper/2406.18145/) (2024)

## Abstract (arXiv)

Local differential privacy (LDP) is a recently proposed privacy standard for collecting and analyzing data, which has been used, e.g., in the Chrome browser, iOS and macOS. In LDP, each user perturbs her information locally, and only sends the randomized version to an aggregator who performs analyses, which protects both the users and the aggregator against private information leaks. Although LDP has attracted much research attention in recent years, the majority of existing work focuses on applying LDP to complex data and/or analysis tasks. In this paper, we point out that the fundamental problem of collecting multidimensional data under LDP has not been addressed sufficiently, and there remains much room for improvement even for basic tasks such as computing the mean value over a single numeric attribute under LDP. Motivated by this, we first propose novel LDP mechanisms for collecting a numeric attribute, whose accuracy is at least no worse (and usually better) than existing solutions in terms of worst-case noise variance. Then, we extend these mechanisms to multidimensional data that can contain both numeric and categorical attributes, where our mechanisms always outperform existing solutions regarding worst-case noise variance. As a case study, we apply our solutions to build an LDP-compliant stochastic gradient descent algorithm (SGD), which powers many important machine learning tasks. Experiments using real datasets confirm the effectiveness of our methods, and their advantages over existing solutions.