# Differentially Private Distributed Bayesian Linear Regression with MCMC

arXiv: https://arxiv.org/abs/2301.13778 · HTML: https://mlsanity.com/paper/2301.13778/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 15 of 15)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1502.07645/) (2015)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis](https://mlsanity.com/paper/1603.07294/) (2016)
- [Differentially Private Simple Linear Regression](https://mlsanity.com/paper/2007.05157/) (2020)
- [Differentially Private Bayesian Linear Regression](https://mlsanity.com/paper/1910.13153/) (2019)
- [Parametric Bootstrap for Differentially Private Confidence Intervals](https://mlsanity.com/paper/2006.07749/) (2020)
- [Differentially Private Markov Chain Monte Carlo](https://mlsanity.com/paper/1901.10275/) (2019)
- [Differentially Private Accelerated Optimization Algorithms](https://mlsanity.com/paper/2008.01989/) (2020)
- [Differentially Private Bayesian Learning on Distributed Data](https://mlsanity.com/paper/1703.01106/) (2017)
- [Data Augmentation MCMC for Bayesian Inference from Privatized Data](https://mlsanity.com/paper/2206.00710/) (2022)
- [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)

- [The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2309.01243/) (2023)

## Abstract (arXiv)

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. Bayesian estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.