# Differentially Private Query Release Through Adaptive Projection

arXiv: https://arxiv.org/abs/2103.06641 · HTML: https://mlsanity.com/paper/2103.06641/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 11 Mar 2021.

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

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [DP-CGAN: Differentially Private Synthetic Data and Label Generation](https://mlsanity.com/paper/2001.09700/) (2020)
- [Graphical-model based estimation and inference for differential privacy](https://mlsanity.com/paper/1901.09136/) (2019)
- [New Oracle-Efficient Algorithms for Private Synthetic Data Release](https://mlsanity.com/paper/2007.05453/) (2020)
- [Practical Differentially Private Top-k Selection with Pay-what-you-get Composition](https://mlsanity.com/paper/1905.04273/) (2019)
- [Optimizing error of high-dimensional statistical queries under differential privacy](https://mlsanity.com/paper/1808.03537/) (2018)
- [Dual Query: Practical Private Query Release for High Dimensional Data](https://mlsanity.com/paper/1402.1526/) (2014)
- [P3GM: Private High-Dimensional Data Release via Privacy Preserving Phased Generative Model](https://mlsanity.com/paper/2006.12101/) (2020)
- [Private Post-GAN Boosting](https://mlsanity.com/paper/2007.11934/) (2020)
- [Efficient Algorithms for Privately Releasing Marginals via Convex Relaxations](https://mlsanity.com/paper/1308.1385/) (2013)
- [Marginal Release Under Local Differential Privacy](https://mlsanity.com/paper/1711.02952/) (2017)
- [Towards Instance-Optimal Private Query Release](https://mlsanity.com/paper/1811.03763/) (2018)
- [How to Use Heuristics for Differential Privacy](https://mlsanity.com/paper/1811.07765/) (2018)
- [Faster Private Release of Marginals on Small Databases](https://mlsanity.com/paper/1304.3754/) (2013)

## Built on by (most cited first, 30 of 52)

- [How to DP-fy ML: A Practical Guide to Machine Learning with Differential Privacy](https://mlsanity.com/paper/2303.00654/) (2023)
- [Iterative Methods for Private Synthetic Data: Unifying Framework and New Methods](https://mlsanity.com/paper/2106.07153/) (2021)
- [SoK: Privacy-Preserving Data Synthesis](https://mlsanity.com/paper/2307.02106/) (2023)
- [Private Synthetic Data for Multitask Learning and Marginal Queries](https://mlsanity.com/paper/2209.07400/) (2022)
- [Privacy-Preserving Instructions for Aligning Large Language Models](https://mlsanity.com/paper/2402.13659/) (2024)
- [A Linear Reconstruction Approach for Attribute Inference Attacks against Synthetic Data](https://mlsanity.com/paper/2301.10053/) (2023)
- [Grounding and Evaluation for Large Language Models: Practical Challenges and Lessons Learned (Survey)](https://mlsanity.com/paper/2407.12858/) (2024)
- [Generating Private Synthetic Data with Genetic Algorithms](https://mlsanity.com/paper/2306.03257/) (2023)
- [Confidence-Ranked Reconstruction of Census Microdata from Published Statistics](https://mlsanity.com/paper/2211.03128/) (2022)
- [Differentially Private Tabular Data Synthesis using Large Language Models](https://mlsanity.com/paper/2406.01457/) (2024)
- [Graphical vs. Deep Generative Models: Measuring the Impact of Differentially Private Mechanisms and Budgets on Utility](https://mlsanity.com/paper/2305.10994/) (2023)
- [CuTS: Customizable Tabular Synthetic Data Generation](https://mlsanity.com/paper/2307.03577/) (2023)
- [The Elusive Pursuit of Reproducing PATE-GAN: Benchmarking, Auditing, Debugging](https://mlsanity.com/paper/2406.13985/) (2024)
- [dpart: Differentially Private Autoregressive Tabular, a General Framework for Synthetic Data Generation](https://mlsanity.com/paper/2207.05810/) (2022)
- [Privacy Vulnerabilities in Marginals-based Synthetic Data](https://mlsanity.com/paper/2410.05506/) (2024)
- [Noise-Aware Statistical Inference with Differentially Private Synthetic Data](https://mlsanity.com/paper/2205.14485/) (2022)
- [Post-processing Private Synthetic Data for Improving Utility on Selected Measures](https://mlsanity.com/paper/2305.15538/) (2023)
- [Synthetic Tabular Data: Methods, Attacks and Defenses](https://mlsanity.com/paper/2506.06108/) (2025)
- [Privacy-preserving data release leveraging optimal transport and particle gradient descent](https://mlsanity.com/paper/2401.17823/) (2024)
- [Joint Selection: Adaptively Incorporating Public Information for Private Synthetic Data](https://mlsanity.com/paper/2403.07797/) (2024)
- [Relaxed Marginal Consistency for Differentially Private Query Answering](https://mlsanity.com/paper/2109.06153/) (2021)
- [QuerySnout: Automating the Discovery of Attribute Inference Attacks against Query-Based Systems](https://mlsanity.com/paper/2211.05249/) (2022)
- [FLAIM: AIM-based Synthetic Data Generation in the Federated Setting](https://mlsanity.com/paper/2310.03447/) (2023)
- [Tabular Data Synthesis with Differential Privacy: A Survey](https://mlsanity.com/paper/2411.03351/) (2024)
- [Is API Access to LLMs Useful for Generating Private Synthetic Tabular Data?](https://mlsanity.com/paper/2502.06555/) (2025)
- [The Importance of Being Discrete: Measuring the Impact of Discretization in End-to-End Differentially Private Synthetic Data](https://mlsanity.com/paper/2504.06923/) (2025)
- [A Simple and Practical Method for Reducing the Disparate Impact of Differential Privacy](https://mlsanity.com/paper/2312.11712/) (2023)
- [Private Regression via Data-Dependent Sufficient Statistic Perturbation](https://mlsanity.com/paper/2405.15002/) (2024)
- [Improving the Generation and Evaluation of Synthetic Data for Downstream Medical Causal Inference](https://mlsanity.com/paper/2510.18768/) (2025)
- [The Tensor Data Platform: Towards an AI-centric Database System](https://mlsanity.com/paper/2211.02753/) (2022)

## Abstract (arXiv)

We propose, implement, and evaluate a new algorithm for releasing answers to very large numbers of statistical queries like k-way marginals, subject to differential privacy. Our algorithm makes adaptive use of a continuous relaxation of the Projection Mechanism, which answers queries on the private dataset using simple perturbation, and then attempts to find the synthetic dataset that most closely matches the noisy answers. We use a continuous relaxation of the synthetic dataset domain which makes the projection loss differentiable, and allows us to use efficient ML optimization techniques and tooling. Rather than answering all queries up front, we make judicious use of our privacy budget by iteratively and adaptively finding queries for which our (relaxed) synthetic data has high error, and then repeating the projection. We perform extensive experimental evaluations across a range of parameters and datasets, and find that our method outperforms existing algorithms in many cases, especially when the privacy budget is small or the query class is large.