# Differentially Private Linear Regression and Synthetic Data Generation with Statistical Guarantees

arXiv: https://arxiv.org/abs/2510.16974 · HTML: https://mlsanity.com/paper/2510.16974/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 19 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Benchmarking Differentially Private Synthetic Data Generation Algorithms](https://mlsanity.com/paper/2112.09238/) (2021)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [Differentially Private Ordinary Least Squares](https://mlsanity.com/paper/1507.02482/) (2015)
- [Differentially Private Simple Linear Regression](https://mlsanity.com/paper/2007.05157/) (2020)
- [PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions](https://mlsanity.com/paper/1601.03229/) (2016)
- [Parametric Bootstrap for Differentially Private Confidence Intervals](https://mlsanity.com/paper/2006.07749/) (2020)
- [Easy Differentially Private Linear Regression](https://mlsanity.com/paper/2208.07353/) (2022)
- [Bayesian Differential Privacy through Posterior Sampling](https://mlsanity.com/paper/1306.1066/) (2013)
- [Benchmarking Differentially Private Tabular Data Synthesis](https://mlsanity.com/paper/2504.14061/) (2025)
- [Differentially Private Regression with Unbounded Covariates](https://mlsanity.com/paper/2202.11199/) (2022)
- [Identification, Amplification and Measurement: A bridge to Gaussian Differential Privacy](https://mlsanity.com/paper/2210.09269/) (2022)
- [Better Private Linear Regression Through Better Private Feature Selection](https://mlsanity.com/paper/2306.00920/) (2023)
- [Statistical Data Privacy: A Song of Privacy and Utility](https://mlsanity.com/paper/2205.03336/) (2022)
- [Differentially Private Linear Regression with Linked Data](https://mlsanity.com/paper/2308.00836/) (2023)
- [To democratize research with sensitive data, we should make synthetic data more accessible](https://mlsanity.com/paper/2404.17271/) (2024)
- [Assessing Utility of Differential Privacy for RCTs](https://mlsanity.com/paper/2309.14581/) (2023)

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

- [Refined Differentially Private Linear Regression via Extension of a Free Lunch Result](https://mlsanity.com/paper/2604.11820/) (2026)

## Abstract (arXiv)

In the social sciences, small- to medium-scale datasets are common, and linear regression is canonical. In privacy-aware settings, much work has focused on differentially private (DP) linear regression, but mostly on point estimation with limited attention to uncertainty quantification. Meanwhile, synthetic data generation (SDG) is increasingly important for reproducibility studies, yet current DP linear regression methods do not readily support it. Mainstream DP-SDG approaches either are tailored to discrete or discretized data, making them less suitable for analyses involving continuous variables, or rely on deep learning models that require large datasets, limiting their use for the smaller-scale data typical in social science. We propose a method for linear regression with valid inference under Gaussian DP. It includes a bias-corrected estimator with asymptotic confidence intervals (CIs) and a general SDG procedure such that the corresponding regression on the synthetic data matches our DP linear regression procedure. Our approach is effective in small- to moderate-dimensional settings. Experiments show that our method (1) improves accuracy over existing methods for DP linear regression, (2) provides valid CIs, and (3) produces more reliable synthetic data for downstream statistical and machine learning tasks than current DP synthesizers.