# Improving the Variance of Differentially Private Randomized Experiments through Clustering

arXiv: https://arxiv.org/abs/2308.00957 · HTML: https://mlsanity.com/paper/2308.00957/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 2 Aug 2023.

## Builds on (most cited first, 10 of 10)

- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Private Learning and Sanitization: Pure vs. Approximate Differential Privacy](https://mlsanity.com/paper/1407.2674/) (2014)
- [Differentially Private k-Means with Constant Multiplicative Error](https://mlsanity.com/paper/1804.08001/) (2018)
- [Label differential privacy via clustering](https://mlsanity.com/paper/2110.02159/) (2021)
- [Differentially-Private Clustering of Easy Instances](https://mlsanity.com/paper/2112.14445/) (2021)
- [Differentially Private Estimation of Heterogeneous Causal Effects](https://mlsanity.com/paper/2202.11043/) (2022)
- [Privacy-Preserving Causal Inference via Inverse Probability Weighting](https://mlsanity.com/paper/1905.12592/) (2019)
- [Locally Private Causal Inference for Randomized Experiments](https://mlsanity.com/paper/2301.01616/) (2023)
- [Cluster-Adaptive Network A/B Testing: From Randomization to Estimation](https://mlsanity.com/paper/2008.08648/) (2020)
- [A Robust, Differentially Private Randomized Experiment for Evaluating Online Educational Programs With Sensitive Student Data](https://mlsanity.com/paper/2112.02452/) (2021)

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

- [General Modular Harness for LLM Agents in Multi-Turn Gaming Environments](https://mlsanity.com/paper/2507.11633/) (2025)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)

## Abstract (arXiv)

Estimating causal effects from randomized experiments is only possible if participants are willing to disclose their potentially sensitive responses. Differential privacy, a widely used framework for ensuring an algorithms privacy guarantees, can encourage participants to share their responses without the risk of de-anonymization. However, many mechanisms achieve differential privacy by adding noise to the original dataset, which reduces the precision of causal effect estimation. This introduces a fundamental trade-off between privacy and variance when performing causal analyses on differentially private data. In this work, we propose a new differentially private mechanism, "Cluster-DP", which leverages a given cluster structure in the data to improve the privacy-variance trade-off. While our results apply to any clustering, we demonstrate that selecting higher-quality clusters, according to a quality metric we introduce, can decrease the variance penalty without compromising privacy guarantees. Finally, we evaluate the theoretical and empirical performance of our Cluster-DP algorithm on both real and simulated data, comparing it to common baselines, including two special cases of our algorithm: its unclustered version and a uniform-prior version.