# Differentially Private Online Bayesian Estimation With Adaptive Truncation

arXiv: https://arxiv.org/abs/2301.08202 · HTML: https://mlsanity.com/paper/2301.08202/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 16 of 16)

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1502.07645/) (2015)
- [On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis](https://mlsanity.com/paper/1603.07294/) (2016)
- [Fisher information under local differential privacy](https://mlsanity.com/paper/2005.10783/) (2020)
- [Differentially Private Bayesian Inference for Exponential Families](https://mlsanity.com/paper/1809.02188/) (2018)
- [Differentially Private Markov Chain Monte Carlo](https://mlsanity.com/paper/1901.10275/) (2019)
- [On Connecting Stochastic Gradient MCMC and Differential Privacy](https://mlsanity.com/paper/1712.09097/) (2017)
- [Differentially Private Bayesian Learning on Distributed Data](https://mlsanity.com/paper/1703.01106/) (2017)
- [Quantifying Differential Privacy under Temporal Correlations](https://mlsanity.com/paper/1610.07543/) (2016)
- [Bounded Space Differentially Private Quantiles](https://mlsanity.com/paper/2201.03380/) (2022)
- [Differentially Private Exponential Random Graphs](https://mlsanity.com/paper/1409.4696/) (2014)
- [Data Augmentation MCMC for Bayesian Inference from Privatized Data](https://mlsanity.com/paper/2206.00710/) (2022)
- [Metropolis-Hastings with Averaged Acceptance Ratios](https://mlsanity.com/paper/2101.01253/) (2020)
- [Differentially Private Hamiltonian Monte Carlo](https://mlsanity.com/paper/2106.09376/) (2021)
- [Statistic Selection and MCMC for Differentially Private Bayesian Estimation](https://mlsanity.com/paper/2203.13377/) (2022)

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

- [Bayesian Frequency Estimation Under Local Differential Privacy With an Adaptive Randomized Response Mechanism](https://mlsanity.com/paper/2405.07020/) (2024)

## Abstract (arXiv)

We propose a novel online and adaptive truncation method for differentially private Bayesian online estimation of a static parameter regarding a population. We assume that sensitive information from individuals is collected sequentially and the inferential aim is to estimate, on-the-fly, a static parameter regarding the population to which those individuals belong. We propose sequential Monte Carlo to perform online Bayesian estimation. When individuals provide sensitive information in response to a query, it is necessary to perturb it with privacy-preserving noise to ensure the privacy of those individuals. The amount of perturbation is proportional to the sensitivity of the query, which is determined usually by the range of the queried information. The truncation technique we propose adapts to the previously collected observations to adjust the query range for the next individual. The idea is that, based on previous observations, we can carefully arrange the interval into which the next individual's information is to be truncated before being perturbed with privacy-preserving noise. In this way, we aim to design predictive queries with small sensitivity, hence small privacy-preserving noise, enabling more accurate estimation while maintaining the same level of privacy. To decide on the location and the width of the interval, we use an exploration-exploitation approach a la Thompson sampling with an objective function based on the Fisher information of the generated observation. We show the merits of our methodology with numerical examples.