# Differentially Private Confidence Intervals for Empirical Risk Minimization

arXiv: https://arxiv.org/abs/1804.03794 · HTML: https://mlsanity.com/paper/1804.03794/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2018.

## Built on by (most cited first, 11 of 11)

- [Survey: Leakage and Privacy at Inference Time](https://mlsanity.com/paper/2107.01614/) (2021)
- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [Private Prediction Sets](https://mlsanity.com/paper/2102.06202/) (2021)
- [Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation](https://mlsanity.com/paper/2402.13531/) (2024)
- [Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies](https://mlsanity.com/paper/2210.06140/) (2022)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Resampling methods for private statistical inference](https://mlsanity.com/paper/2402.07131/) (2024)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)
- [Differentially Private Nonparametric Confidence Intervals Under Minimal Distributional Assumptions](https://mlsanity.com/paper/2511.01303/) (2025)
- [DPpack: An R Package for Differentially Private Statistical Analysis and Machine Learning](https://mlsanity.com/paper/2309.10965/) (2023)
- [Near-Optimal Private Tests for Simple and MLR Hypotheses](https://mlsanity.com/paper/2601.21959/) (2026)

## Abstract (arXiv)

The process of data mining with differential privacy produces results that are affected by two types of noise: sampling noise due to data collection and privacy noise that is designed to prevent the reconstruction of sensitive information. In this paper, we consider the problem of designing confidence intervals for the parameters of a variety of differentially private machine learning models. The algorithms can provide confidence intervals that satisfy differential privacy (as well as the more recently proposed concentrated differential privacy) and can be used with existing differentially private mechanisms that train models using objective perturbation and output perturbation.