# Locally Differentially Private Frequency Estimation with Consistency

arXiv: https://arxiv.org/abs/1905.08320 · HTML: https://mlsanity.com/paper/1905.08320/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2019.

## Built on by (most cited first, 12 of 12)

- [DP-TabICL: In-Context Learning with Differentially Private Tabular Data](https://mlsanity.com/paper/2403.05681/) (2024)
- [Fine-grained Poisoning Attack to Local Differential Privacy Protocols for Mean and Variance Estimation](https://mlsanity.com/paper/2205.11782/) (2022)
- [On the Robustness of LDP Protocols for Numerical Attributes under Data Poisoning Attacks](https://mlsanity.com/paper/2403.19510/) (2024)
- [Two Views of Constrained Differential Privacy: Belief Revision and Update](https://mlsanity.com/paper/2303.00228/) (2023)
- [Locally Differentially Private Bayesian Inference](https://mlsanity.com/paper/2110.14426/) (2021)
- [On the Utility Gain of Iterative Bayesian Update for Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2307.07744/) (2023)
- [Bayesian Frequency Estimation Under Local Differential Privacy With an Adaptive Randomized Response Mechanism](https://mlsanity.com/paper/2405.07020/) (2024)
- [Data Poisoning Attacks to Locally Differentially Private Range Query Protocols](https://mlsanity.com/paper/2503.03454/) (2025)
- [Mitigating Data Poisoning Attacks to Local Differential Privacy](https://mlsanity.com/paper/2506.02156/) (2025)
- [Consistent Estimation of Numerical Distributions under Local Differential Privacy by Wavelet Expansion](https://mlsanity.com/paper/2509.19661/) (2025)
- [Jacobian-Guided Anisotropic Noise Reshaping for Enhancing Representation Utility under Local Differential Privacy](https://mlsanity.com/paper/2605.16812/) (2026)
- [Robust Estimation of Sparse Numerical Vectors under Local Differential Privacy](https://mlsanity.com/paper/2607.27815/) (2026)

## Abstract (arXiv)

Local Differential Privacy (LDP) protects user privacy from the data collector. LDP protocols have been increasingly deployed in the industry. A basic building block is frequency oracle (FO) protocols, which estimate frequencies of values. While several FO protocols have been proposed, the design goal does not lead to optimal results for answering many queries. In this paper, we show that adding post-processing steps to FO protocols by exploiting the knowledge that all individual frequencies should be non-negative and they sum up to one can lead to significantly better accuracy for a wide range of tasks, including frequencies of individual values, frequencies of the most frequent values, and frequencies of subsets of values. We consider 10 different methods that exploit this knowledge differently. We establish theoretical relationships between some of them and conducted extensive experimental evaluations to understand which methods should be used for different query tasks.