# Simulation-based Bayesian Inference from Privacy Protected Data

arXiv: https://arxiv.org/abs/2310.12781 · HTML: https://mlsanity.com/paper/2310.12781/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 59 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Differentially Private Stochastic Optimization: New Results in Convex and Non-Convex Settings](https://mlsanity.com/paper/2107.05585/) (2021)
- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis](https://mlsanity.com/paper/1603.07294/) (2016)
- [Faster Rates of Convergence to Stationary Points in Differentially Private Optimization](https://mlsanity.com/paper/2206.00846/) (2022)
- [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)
- [Private GANs, Revisited](https://mlsanity.com/paper/2302.02936/) (2023)
- [Differentially Private Bayesian Inference for Generalized Linear Models](https://mlsanity.com/paper/2011.00467/) (2020)
- [Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy](https://mlsanity.com/paper/2110.14465/) (2021)
- [Differentially private significance tests for regression coefficients](https://mlsanity.com/paper/1705.09561/) (2017)
- [Differentially Private Normalizing Flows for Privacy-Preserving Density Estimation](https://mlsanity.com/paper/2103.14068/) (2021)
- [Differential Privacy for Government Agencies -- Are We There Yet?](https://mlsanity.com/paper/2102.08847/) (2021)
- [Data Augmentation MCMC for Bayesian Inference from Privatized Data](https://mlsanity.com/paper/2206.00710/) (2022)
- [Hypothesis Testing for Differentially Private Linear Regression](https://mlsanity.com/paper/2206.14449/) (2022)
- [Simulation-based, Finite-sample Inference for Privatized Data](https://mlsanity.com/paper/2303.05328/) (2023)
- [Private Posterior distributions from Variational approximations](https://mlsanity.com/paper/1511.07896/) (2015)
- [Differentially Private Synthetic Control](https://mlsanity.com/paper/2303.14084/) (2023)

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

- [Noise-Aware Differentially Private Variational Inference](https://mlsanity.com/paper/2410.19371/) (2024)

## Abstract (arXiv)

Many modern statistical analysis and machine learning applications require training models on sensitive user data. Under a formal definition of privacy protection, differentially private algorithms inject calibrated noise into the confidential data or during the data analysis process to produce privacy-protected datasets or queries. However, restricting access to only privatized data during statistical analysis makes it computationally challenging to make valid statistical inferences. In this work, we propose simulation-based inference methods from privacy-protected datasets. In addition to sequential Monte Carlo approximate Bayesian computation, we adopt neural conditional density estimators as a flexible family of distributions to approximate the posterior distribution of model parameters given the observed private query results. We illustrate our methods on discrete time-series data under an infectious disease model and with ordinary linear regression models. Illustrating the privacy-utility trade-off, our experiments and analysis demonstrate the necessity and feasibility of designing valid statistical inference procedures to correct for biases introduced by the privacy-protection mechanisms.