# Differentially private significance tests for regression coefficients

arXiv: https://arxiv.org/abs/1705.09561 · HTML: https://mlsanity.com/paper/1705.09561/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2017.

## Built on by (most cited first, 12 of 12)

- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [Differentially Private Regression with Unbounded Covariates](https://mlsanity.com/paper/2202.11199/) (2022)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Improved Analysis of Sparse Linear Regression in Local Differential Privacy Model](https://mlsanity.com/paper/2310.07367/) (2023)
- [Differentially Private Estimation via Statistical Depth](https://mlsanity.com/paper/2207.12602/) (2022)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)
- [Recycling Scraps: Improving Private Learning by Leveraging Intermediate Checkpoints](https://mlsanity.com/paper/2210.01864/) (2022)
- [Simulation-based Bayesian Inference from Privacy Protected Data](https://mlsanity.com/paper/2310.12781/) (2023)
- [Differentially private Bayesian tests](https://mlsanity.com/paper/2401.15502/) (2024)
- [Differentially Private Conditional Independence Testing](https://mlsanity.com/paper/2306.06721/) (2023)
- [DPpack: An R Package for Differentially Private Statistical Analysis and Machine Learning](https://mlsanity.com/paper/2309.10965/) (2023)

## Abstract (arXiv)

Many data producers seek to provide users access to confidential data without unduly compromising data subjects' privacy and confidentiality. One general strategy is to require users to do analyses without seeing the confidential data; for example, analysts only get access to synthetic data or query systems that provide disclosure-protected outputs of statistical models. With synthetic data or redacted outputs, the analyst never really knows how much to trust the resulting findings. In particular, if the user did the same analysis on the confidential data, would regression coefficients of interest be statistically significant or not? We present algorithms for assessing this question that satisfy differential privacy. We describe conditions under which the algorithms should give accurate answers about statistical significance. We illustrate the properties of the proposed methods using artificial and genuine data.