# Private Synthetic Data with Hierarchical Structure

arXiv: https://arxiv.org/abs/2206.05942 · HTML: https://mlsanity.com/paper/2206.05942/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 17 of 17)

- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [AIM: An Adaptive and Iterative Mechanism for Differentially Private Synthetic Data](https://mlsanity.com/paper/2201.12677/) (2022)
- [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)
- [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)
- [Leveraging Public Data for Practical Private Query Release](https://mlsanity.com/paper/2102.08598/) (2021)
- [Differentially Private Synthetic Data: Applied Evaluations and Enhancements](https://mlsanity.com/paper/2011.05537/) (2020)
- [The Power of Factorization Mechanisms in Local and Central Differential Privacy](https://mlsanity.com/paper/1911.08339/) (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)
- [Private Post-GAN Boosting](https://mlsanity.com/paper/2007.11934/) (2020)
- [Private Multiplicative Weights Beyond Linear Queries](https://mlsanity.com/paper/1407.1571/) (2014)
- [Bounding, Concentrating, and Truncating: Unifying Privacy Loss Composition for Data Analytics](https://mlsanity.com/paper/2004.07223/) (2020)

## Built on by (most cited first, 2 of 2)

- [Summary Statistic Privacy in Data Sharing](https://mlsanity.com/paper/2303.02014/) (2023)
- [ResidualPlanner+: a scalable matrix mechanism for marginals and beyond](https://mlsanity.com/paper/2305.08175/) (2023)

## Abstract (arXiv)

We study the problem of differentially private synthetic data generation for hierarchical datasets in which individual data points are grouped together (e.g., people within households). In particular, to measure the similarity between the synthetic dataset and the underlying private one, we frame our objective under the problem of private query release, generating a synthetic dataset that preserves answers for some collection of queries (i.e., statistics like mean aggregate counts). However, while the application of private synthetic data to the problem of query release has been well studied, such research is restricted to non-hierarchical data domains, raising the initial question -- what queries are important when considering data of this form? Moreover, it has not yet been established how one can generate synthetic data at both the group and individual-level while capturing such statistics. In light of these challenges, we first formalize the problem of hierarchical query release, in which the goal is to release a collection of statistics for some hierarchical dataset. Specifically, we provide a general set of statistical queries that captures relationships between attributes at both the group and individual-level. Subsequently, we introduce private synthetic data algorithms for hierarchical query release and evaluate them on hierarchical datasets derived from the American Community Survey and Allegheny Family Screening Tool data. Finally, we look to the American Community Survey, whose inherent hierarchical structure gives rise to another set of domain-specific queries that we run experiments with.