# Privacy Amplification Via Bernoulli Sampling

arXiv: https://arxiv.org/abs/2105.10594 · HTML: https://mlsanity.com/paper/2105.10594/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 21 May 2021.

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

- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Subsampled R'enyi Differential Privacy and Analytical Moments Accountant](https://mlsanity.com/paper/1808.00087/) (2018)
- [R'enyi Differential Privacy of the Sampled Gaussian Mechanism](https://mlsanity.com/paper/1908.10530/) (2019)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Privacy Amplification by Iteration](https://mlsanity.com/paper/1808.06651/) (2018)
- [The Privacy Blanket of the Shuffle Model](https://mlsanity.com/paper/1903.02837/) (2019)
- [Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1502.07645/) (2015)
- [Differentially Private Release and Learning of Threshold Functions](https://mlsanity.com/paper/1504.07553/) (2015)
- [On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis](https://mlsanity.com/paper/1603.07294/) (2016)
- [Privacy Amplification by Mixing and Diffusion Mechanisms](https://mlsanity.com/paper/1905.12264/) (2019)
- [Characterizing the Sample Complexity of Private Learners](https://mlsanity.com/paper/1402.2224/) (2014)
- [Bayesian Differential Privacy through Posterior Sampling](https://mlsanity.com/paper/1306.1066/) (2013)
- [R'enyi Differential Privacy Mechanisms for Posterior Sampling](https://mlsanity.com/paper/1710.00892/) (2017)

## Built on by (most cited first, 4 of 4)

- [Sparse Random Networks for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2209.15328/) (2022)
- [Differentially Private Natural Language Models: Recent Advances and Future Directions](https://mlsanity.com/paper/2301.09112/) (2023)
- [PRISM: Privacy-Preserving Improved Stochastic Masking for Federated Generative Models](https://mlsanity.com/paper/2503.08085/) (2025)
- [Towards Privacy-Preserving and Heterogeneity-aware Split Federated Learning via Probabilistic Masking](https://mlsanity.com/paper/2509.14603/) (2025)

## Abstract (arXiv)

Balancing privacy and accuracy is a major challenge in designing differentially private machine learning algorithms. One way to improve this tradeoff for free is to leverage the noise in common data operations that already use randomness. Such operations include noisy SGD and data subsampling. The additional noise in these operations may amplify the privacy guarantee of the overall algorithm, a phenomenon known as privacy amplification. In this paper, we analyze the privacy amplification of sampling from a multidimensional Bernoulli distribution family given the parameter from a private algorithm. This setup has applications to Bayesian inference and to data compression. We provide an algorithm to compute the amplification factor, and we establish upper and lower bounds on this factor.