# Noise-Aware Statistical Inference with Differentially Private Synthetic Data arXiv: https://arxiv.org/abs/2205.14485 ยท HTML: https://mlsanity.com/paper/2205.14485/ ## Key facts - Cited by 9 papers in the map (data through 14 Oct 2026). - Builds on 29 of its 69 references that are in the map. - First posted on arXiv 28 May 2022. ## Builds on (most cited first, 29 of 29) - [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013) - [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018) - [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018) - [GS-WGAN: A Gradient-Sanitized Approach for Learning Differentially Private Generators](https://mlsanity.com/paper/2006.08265/) (2020) - [Winning the NIST Contest: A scalable and general approach to differentially private synthetic data](https://mlsanity.com/paper/2108.04978/) (2021) - [AIM: An Adaptive and Iterative Mechanism for Differentially Private Synthetic Data](https://mlsanity.com/paper/2201.12677/) (2022) - [Benchmarking Differentially Private Synthetic Data Generation Algorithms](https://mlsanity.com/paper/2112.09238/) (2021) - [DP-MERF: Differentially Private Mean Embeddings with Random Features for Practical Privacy-Preserving Data Generation](https://mlsanity.com/paper/2002.11603/) (2020) - [Graphical-model based estimation and inference for differential privacy](https://mlsanity.com/paper/1901.09136/) (2019) - [Iterative Methods for Private Synthetic Data: Unifying Framework and New Methods](https://mlsanity.com/paper/2106.07153/) (2021) - [G-PATE: Scalable Differentially Private Data Generator via Private Aggregation of Teacher Discriminators](https://mlsanity.com/paper/1906.09338/) (2019) - [Differentially Private Query Release Through Adaptive Projection](https://mlsanity.com/paper/2103.06641/) (2021) - [New Oracle-Efficient Algorithms for Private Synthetic Data Release](https://mlsanity.com/paper/2007.05453/) (2020) - [Optimizing error of high-dimensional statistical queries under differential privacy](https://mlsanity.com/paper/1808.03537/) (2018) - [Differentially Private Bayesian Linear Regression](https://mlsanity.com/paper/1910.13153/) (2019) - [PEARL: Data Synthesis via Private Embeddings and Adversarial Reconstruction Learning](https://mlsanity.com/paper/2106.04590/) (2021) - [PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions](https://mlsanity.com/paper/1601.03229/) (2016) - [Private Post-GAN Boosting](https://mlsanity.com/paper/2007.11934/) (2020) - [Parametric Bootstrap for Differentially Private Confidence Intervals](https://mlsanity.com/paper/2006.07749/) (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) - [Differentially Private Variational Inference for Non-conjugate Models](https://mlsanity.com/paper/1610.08749/) (2016) - [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) - [Foundations of Bayesian Learning from Synthetic Data](https://mlsanity.com/paper/2011.08299/) (2020) - [Privacy-preserving data sharing via probabilistic modelling](https://mlsanity.com/paper/1912.04439/) (2019) - [Differentially Private Learning of Undirected Graphical Models using Collective Graphical Models](https://mlsanity.com/paper/1706.04646/) (2017) - [Model-based Differentially Private Data Synthesis and Statistical Inference in Multiply Synthetic Differentially Private Data](https://mlsanity.com/paper/1606.08052/) (2016) - [A Latent Class Modeling Approach for Generating Synthetic Data and Making Posterior Inferences from Differentially Private Counts](https://mlsanity.com/paper/2201.10545/) (2022) ## Built on by (most cited first, 9 of 9) - [The Real Deal Behind the Artificial Appeal: Inferential Utility of Tabular Synthetic Data](https://mlsanity.com/paper/2312.07837/) (2023) - [Does Differentially Private Synthetic Data Lead to Synthetic Discoveries?](https://mlsanity.com/paper/2403.13612/) (2024) - [Debiasing Synthetic Data Generated by Deep Generative Models](https://mlsanity.com/paper/2411.04216/) (2024) - [A Bias-Variance Decomposition for Ensembles over Multiple Synthetic Datasets](https://mlsanity.com/paper/2402.03985/) (2024) - [Collaborative Learning From Distributed Data With Differentially Private Synthetic Twin Data](https://mlsanity.com/paper/2308.04755/) (2023) - [Inference With Combining Rules From Multiple Differentially Private Synthetic Datasets](https://mlsanity.com/paper/2405.04769/) (2024) - [Noise-Aware Differentially Private Variational Inference](https://mlsanity.com/paper/2410.19371/) (2024) - [Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Families](https://mlsanity.com/paper/2603.02010/) (2026) - [Workload-Preserving Differentially Private Synthetic Data for Causal Inference via Maximum-Entropy Calibration](https://mlsanity.com/paper/2607.08122/) (2026) ## Abstract (arXiv) While generation of synthetic data under differential privacy (DP) has received a lot of attention in the data privacy community, analysis of synthetic data has received much less. Existing work has shown that simply analysing DP synthetic data as if it were real does not produce valid inferences of population-level quantities. For example, confidence intervals become too narrow, which we demonstrate with a simple experiment. We tackle this problem by combining synthetic data analysis techniques from the field of multiple imputation (MI), and synthetic data generation using noise-aware (NA) Bayesian modeling into a pipeline NA+MI that allows computing accurate uncertainty estimates for population-level quantities from DP synthetic data. To implement NA+MI for discrete data generation using the values of marginal queries, we develop a novel noise-aware synthetic data generation algorithm NAPSU-MQ using the principle of maximum entropy. Our experiments demonstrate that the pipeline is able to produce accurate confidence intervals from DP synthetic data. The intervals become wider with tighter privacy to accurately capture the additional uncertainty stemming from DP noise.