# Personalized Differential Privacy for Ridge Regression

arXiv: https://arxiv.org/abs/2401.17127 · HTML: https://mlsanity.com/paper/2401.17127/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 15 of 15)

- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [Differentially Private Learning Needs Better Features (or Much More Data)](https://mlsanity.com/paper/2011.11660/) (2020)
- [Private Stochastic Convex Optimization with Optimal Rates](https://mlsanity.com/paper/1908.09970/) (2019)
- [Understanding Gradient Clipping in Private SGD: A Geometric Perspective](https://mlsanity.com/paper/2006.15429/) (2020)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [Differentially Private Simple Linear Regression](https://mlsanity.com/paper/2007.05157/) (2020)
- [Heterogeneous Differential Privacy](https://mlsanity.com/paper/1504.06998/) (2015)
- [Evading Curse of Dimensionality in Unconstrained Private GLMs via Private Gradient Descent](https://mlsanity.com/paper/2006.06783/) (2020)
- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [Have it your way: Individualized Privacy Assignment for DP-SGD](https://mlsanity.com/paper/2303.17046/) (2023)
- [Differentially Private Generalized Linear Models Revisited](https://mlsanity.com/paper/2205.03014/) (2022)
- [Property Testing for Differential Privacy](https://mlsanity.com/paper/1806.06427/) (2018)
- [Optimal Data Acquisition with Privacy-Aware Agents](https://mlsanity.com/paper/2209.06340/) (2022)
- [Individualized PATE: Differentially Private Machine Learning with Individual Privacy Guarantees](https://mlsanity.com/paper/2202.10517/) (2022)
- [Individual Sensitivity Preprocessing for Data Privacy](https://mlsanity.com/paper/1804.08645/) (2018)

## Built on by (most cited first, 3 of 3)

- [Private Estimation when Data and Privacy Demands are Correlated](https://mlsanity.com/paper/2407.11274/) (2024)
- [Differentially Private Random Feature Model](https://mlsanity.com/paper/2412.04785/) (2024)
- [Managing Correlations in Data and Privacy Demand](https://mlsanity.com/paper/2509.02856/) (2025)

## Abstract (arXiv)

The increased application of machine learning (ML) in sensitive domains requires protecting the training data through privacy frameworks, such as differential privacy (DP). DP requires to specify a uniform privacy level varepsilon that expresses the maximum privacy loss that each data point in the entire dataset is willing to tolerate. Yet, in practice, different data points often have different privacy requirements. Having to set one uniform privacy level is usually too restrictive, often forcing a learner to guarantee the stringent privacy requirement, at a large cost to accuracy. To overcome this limitation, we introduce our novel Personalized-DP Output Perturbation method (PDP-OP) that enables to train Ridge regression models with individual per data point privacy levels. We provide rigorous privacy proofs for our PDP-OP as well as accuracy guarantees for the resulting model. This work is the first to provide such theoretical accuracy guarantees when it comes to personalized DP in machine learning, whereas previous work only provided empirical evaluations. We empirically evaluate PDP-OP on synthetic and real datasets and with diverse privacy distributions. We show that by enabling each data point to specify their own privacy requirement, we can significantly improve the privacy-accuracy trade-offs in DP. We also show that PDP-OP outperforms the personalized privacy techniques of Jorgensen et al. (2015).