# Privacy-preserving parametric inference: a case for robust statistics

arXiv: https://arxiv.org/abs/1911.10167 · HTML: https://mlsanity.com/paper/1911.10167/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2019.

## Built on by (most cited first, 18 of 18)

- [Differential privacy and robust statistics in high dimensions](https://mlsanity.com/paper/2111.06578/) (2021)
- [Robustness Implies Privacy in Statistical Estimation](https://mlsanity.com/paper/2212.05015/) (2022)
- [Membership Inference Attacks and Defenses in Federated Learning: A Survey](https://mlsanity.com/paper/2412.06157/) (2024)
- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning](https://mlsanity.com/paper/2303.07152/) (2023)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Distribution-Invariant Differential Privacy](https://mlsanity.com/paper/2111.05791/) (2021)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Mitigating Statistical Bias within Differentially Private Synthetic Data](https://mlsanity.com/paper/2108.10934/) (2021)
- [Statistic Selection and MCMC for Differentially Private Bayesian Estimation](https://mlsanity.com/paper/2203.13377/) (2022)
- [High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guarantees](https://mlsanity.com/paper/2104.00245/) (2021)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)
- [One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation](https://mlsanity.com/paper/2202.07194/) (2022)
- [Robust probabilistic inference via a constrained transport metric](https://mlsanity.com/paper/2303.10085/) (2023)
- [Differentially Private Topological Data Analysis](https://mlsanity.com/paper/2305.03609/) (2023)
- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)
- [Differentially Private Statistical Inference through β-Divergence One Posterior Sampling](https://mlsanity.com/paper/2307.05194/) (2023)
- [Pre-Training Estimators for Structural Models: Application to Consumer Search](https://mlsanity.com/paper/2505.00526/) (2025)

## Abstract (arXiv)

Differential privacy is a cryptographically-motivated approach to privacy that has become a very active field of research over the last decade in theoretical computer science and machine learning. In this paradigm one assumes there is a trusted curator who holds the data of individuals in a database and the goal of privacy is to simultaneously protect individual data while allowing the release of global characteristics of the database. In this setting we introduce a general framework for parametric inference with differential privacy guarantees. We first obtain differentially private estimators based on bounded influence M-estimators by leveraging their gross-error sensitivity in the calibration of a noise term added to them in order to ensure privacy. We then show how a similar construction can also be applied to construct differentially private test statistics analogous to the Wald, score and likelihood ratio tests. We provide statistical guarantees for all our proposals via an asymptotic analysis. An interesting consequence of our results is to further clarify the connection between differential privacy and robust statistics. In particular, we demonstrate that differential privacy is a weaker stability requirement than infinitesimal robustness, and show that robust M-estimators can be easily randomized in order to guarantee both differential privacy and robustness towards the presence of contaminated data. We illustrate our results both on simulated and real data.