# Locally Differentially Private Bayesian Inference

arXiv: https://arxiv.org/abs/2110.14426 · HTML: https://mlsanity.com/paper/2110.14426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 67 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 30 of 33)

- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1502.07645/) (2015)
- [Collecting and Analyzing Multidimensional Data with Local Differential Privacy](https://mlsanity.com/paper/1907.00782/) (2019)
- [Local, Private, Efficient Protocols for Succinct Histograms](https://mlsanity.com/paper/1504.04686/) (2015)
- [On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis](https://mlsanity.com/paper/1603.07294/) (2016)
- [Practical Locally Private Heavy Hitters](https://mlsanity.com/paper/1707.04982/) (2017)
- [A Comprehensive Survey on Local Differential Privacy Toward Data Statistics and Analysis](https://mlsanity.com/paper/2010.05253/) (2020)
- [Collecting and Analyzing Data from Smart Device Users with Local Differential Privacy](https://mlsanity.com/paper/1606.05053/) (2016)
- [Differentially Private Bayesian Linear Regression](https://mlsanity.com/paper/1910.13153/) (2019)
- [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)
- [Estimating Numerical Distributions under Local Differential Privacy](https://mlsanity.com/paper/1912.01051/) (2019)
- [Building a RAPPOR with the Unknown: Privacy-Preserving Learning of Associations and Data Dictionaries](https://mlsanity.com/paper/1503.01214/) (2015)
- [Differentially Private Variational Inference for Non-conjugate Models](https://mlsanity.com/paper/1610.08749/) (2016)
- [On Connecting Stochastic Gradient MCMC and Differential Privacy](https://mlsanity.com/paper/1712.09097/) (2017)
- [Differentially Private Bayesian Inference for Generalized Linear Models](https://mlsanity.com/paper/2011.00467/) (2020)
- [Empirical Risk Minimization in the Non-interactive Local Model of Differential Privacy](https://mlsanity.com/paper/2011.05934/) (2020)
- [BLENDER: Enabling Local Search with a Hybrid Differential Privacy Model](https://mlsanity.com/paper/1705.00831/) (2017)
- [PASS-GLM: polynomial approximate sufficient statistics for scalable Bayesian GLM inference](https://mlsanity.com/paper/1709.09216/) (2017)
- [Answering Range Queries Under Local Differential Privacy](https://mlsanity.com/paper/1812.10942/) (2018)
- [Locally Differentially Private Frequency Estimation with Consistency](https://mlsanity.com/paper/1905.08320/) (2019)
- [Variational Bayes In Private Settings (VIPS)](https://mlsanity.com/paper/1611.00340/) (2016)
- [Marginal Release Under Local Differential Privacy](https://mlsanity.com/paper/1711.02952/) (2017)
- [Locally Private Bayesian Inference for Count Models](https://mlsanity.com/paper/1803.08471/) (2018)
- [Locally Private Gaussian Estimation](https://mlsanity.com/paper/1811.08382/) (2018)

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

- [Incentives in Private Collaborative Machine Learning](https://mlsanity.com/paper/2404.01676/) (2024)

## Abstract (arXiv)

In recent years, local differential privacy (LDP) has emerged as a technique of choice for privacy-preserving data collection in several scenarios when the aggregator is not trustworthy. LDP provides client-side privacy by adding noise at the user's end. Thus, clients need not rely on the trustworthiness of the aggregator. In this work, we provide a noise-aware probabilistic modeling framework, which allows Bayesian inference to take into account the noise added for privacy under LDP, conditioned on locally perturbed observations. Stronger privacy protection (compared to the central model) provided by LDP protocols comes at a much harsher privacy-utility trade-off. Our framework tackles several computational and statistical challenges posed by LDP for accurate uncertainty quantification under Bayesian settings. We demonstrate the efficacy of our framework in parameter estimation for univariate and multi-variate distributions as well as logistic and linear regression.