# RPWithPrior: Label Differential Privacy in Regression

arXiv: https://arxiv.org/abs/2601.22625 · HTML: https://mlsanity.com/paper/2601.22625/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 18 of 18)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Deep Learning with Label Differential Privacy](https://mlsanity.com/paper/2102.06062/) (2021)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Antipodes of Label Differential Privacy: PATE and ALIBI](https://mlsanity.com/paper/2106.03408/) (2021)
- [Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spaces](https://mlsanity.com/paper/2211.14400/) (2022)
- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [Label differential privacy via clustering](https://mlsanity.com/paper/2110.02159/) (2021)
- [Reacting to Variations in Product Demand: An Application for Conversion Rate (CR) Prediction in Sponsored Search](https://mlsanity.com/paper/1806.08211/) (2018)
- [Context-Aware Local Differential Privacy](https://mlsanity.com/paper/1911.00038/) (2019)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)
- [Regression with Label Differential Privacy](https://mlsanity.com/paper/2212.06074/) (2022)
- [Differentially Private Regression and Classification with Sparse Gaussian Processes](https://mlsanity.com/paper/1909.09147/) (2019)
- [The Laplace Mechanism has optimal utility for differential privacy over continuous queries](https://mlsanity.com/paper/2105.07176/) (2021)
- [Optimal Unbiased Randomizers for Regression with Label Differential Privacy](https://mlsanity.com/paper/2312.05659/) (2023)

## Built on by (most cited first, 1 of 1)

- [BlockRR: A Unified Framework of RR-type Algorithms for Label Differential Privacy](https://mlsanity.com/paper/2602.03277/) (2026)

## Abstract (arXiv)

With the wide application of machine learning techniques in practice, privacy preservation has gained increasing attention. Protecting user privacy with minimal accuracy loss is a fundamental task in the data analysis and mining community. In this paper, we focus on regression tasks under ε-label differential privacy guarantees. Some existing methods for regression with ε-label differential privacy, such as the RR-On-Bins mechanism, discretized the output space into finite bins and then applied RR algorithm. To efficiently determine these finite bins, the authors rounded the original responses down to integer values. However, such operations does not align well with real-world scenarios. To overcome these limitations, we model both original and randomized responses as continuous random variables, avoiding discretization entirely. Our novel approach estimates an optimal interval for randomized responses and introduces new algorithms designed for scenarios where a prior is either known or unknown. Additionally, we prove that our algorithm, RPWithPrior, guarantees ε-label differential privacy. Numerical results demonstrate that our approach gets better performance compared with the Gaussian, Laplace, Staircase, and RRonBins, Unbiased mechanisms on the Communities and Crime, Criteo Sponsored Search Conversion Log, California Housing datasets.