# Combining Public and Private Data

arXiv: https://arxiv.org/abs/2111.00115 · HTML: https://mlsanity.com/paper/2111.00115/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 6 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 1 of 1)

- [Heterogeneous Differential Privacy](https://mlsanity.com/paper/1504.06998/) (2015)

## Built on by (most cited first, 9 of 9)

- [Optimal Differentially Private Model Training with Public Data](https://mlsanity.com/paper/2306.15056/) (2023)
- [Pre-training Differentially Private Models with Limited Public Data](https://mlsanity.com/paper/2402.18752/) (2024)
- [Mean Estimation Under Heterogeneous Privacy: Some Privacy Can Be Free](https://mlsanity.com/paper/2305.09668/) (2023)
- [Mean Estimation Under Heterogeneous Privacy Demands](https://mlsanity.com/paper/2310.13137/) (2023)
- [Coupling public and private gradient provably helps optimization](https://mlsanity.com/paper/2310.01304/) (2023)
- [Private Estimation when Data and Privacy Demands are Correlated](https://mlsanity.com/paper/2407.11274/) (2024)
- [Managing Correlations in Data and Privacy Demand](https://mlsanity.com/paper/2509.02856/) (2025)
- [Enhancing Differentially Private Linear Regression via Public Second-Moment](https://mlsanity.com/paper/2508.18037/) (2025)
- [Differentially Private Truncation of Unbounded Data via Public Second Moments](https://mlsanity.com/paper/2602.22282/) (2026)

## Abstract (arXiv)

Differential privacy is widely adopted to provide provable privacy guarantees in data analysis. We consider the problem of combining public and private data (and, more generally, data with heterogeneous privacy needs) for estimating aggregate statistics. We introduce a mixed estimator of the mean optimized to minimize the variance. We argue that our mechanism is preferable to techniques that preserve the privacy of individuals by subsampling data proportionally to the privacy needs of users. Similarly, we present a mixed median estimator based on the exponential mechanism. We compare our mechanisms to the methods proposed in Jorgensen et al. [2015]. Our experiments provide empirical evidence that our mechanisms often outperform the baseline methods.