# On the Utility Gain of Iterative Bayesian Update for Locally Differentially Private Mechanisms

arXiv: https://arxiv.org/abs/2307.07744 · HTML: https://mlsanity.com/paper/2307.07744/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 15 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Discrete Distribution Estimation under Local Privacy](https://mlsanity.com/paper/1602.07387/) (2016)
- [Local, Private, Efficient Protocols for Succinct Histograms](https://mlsanity.com/paper/1504.04686/) (2015)
- [Optimal Schemes for Discrete Distribution Estimation under Locally Differential Privacy](https://mlsanity.com/paper/1702.00610/) (2017)
- [Building a RAPPOR with the Unknown: Privacy-Preserving Learning of Associations and Data Dictionaries](https://mlsanity.com/paper/1503.01214/) (2015)
- [Differential Privacy in the Shuffle Model: A Survey of Separations](https://mlsanity.com/paper/2107.11839/) (2021)
- [Locally Differentially Private Frequency Estimation with Consistency](https://mlsanity.com/paper/1905.08320/) (2019)
- [Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates](https://mlsanity.com/paper/2111.04636/) (2021)
- [Multi-Freq-LDPy: Multiple Frequency Estimation Under Local Differential Privacy in Python](https://mlsanity.com/paper/2205.02648/) (2022)
- [On the Risks of Collecting Multidimensional Data Under Local Differential Privacy](https://mlsanity.com/paper/2209.01684/) (2022)
- [Reconstruction of the distribution of sensitive data under free-will privacy](https://mlsanity.com/paper/2208.11268/) (2022)
- [Frequency Estimation of Evolving Data Under Local Differential Privacy](https://mlsanity.com/paper/2210.00262/) (2022)

## Built on by (most cited first, 1 of 1)

- [Enhancing Differentially Private Mechanisms via Empirical Bayes](https://mlsanity.com/paper/2606.21107/) (2026)

## Abstract (arXiv)

This paper investigates the utility gain of using Iterative Bayesian Update (IBU) for private discrete distribution estimation using data obfuscated with Locally Differentially Private (LDP) mechanisms. We compare the performance of IBU to Matrix Inversion (MI), a standard estimation technique, for seven LDP mechanisms designed for one-time data collection and for other seven LDP mechanisms designed for multiple data collections (e.g., RAPPOR). To broaden the scope of our study, we also varied the utility metric, the number of users n, the domain size k, and the privacy parameter ε, using both synthetic and real-world data. Our results suggest that IBU can be a useful post-processing tool for improving the utility of LDP mechanisms in different scenarios without any additional privacy cost. For instance, our experiments show that IBU can provide better utility than MI, especially in high privacy regimes (i.e., when ε is small). Our paper provides insights for practitioners to use IBU in conjunction with existing LDP mechanisms for more accurate and privacy-preserving data analysis. Finally, we implemented IBU for all fourteen LDP mechanisms into the state-of-the-art multi-freq-ldpy Python package (https://pypi.org/project/multi-freq-ldpy/) and open-sourced all our code used for the experiments as tutorials.