Study Compares Differential Privacy and PAC Privacy for Linear Regression Models

Global: Comparison of Differential Privacy and PAC Privacy in Linear Regression

A recent study released on arXiv examines the performance of linear regression models trained under two privacy frameworks—differential privacy and PAC privacy. The paper, authored by Hillary Yang and Yuntao Du, was first submitted on December 3, 2024 and revised on December 30, 2025. Researchers aim to determine how each approach affects model accuracy across real‑world datasets while preserving the confidentiality of individual data points.

Privacy in Statistical Modeling

Linear regression remains a cornerstone technique for predictive analytics, yet its reliance on raw data raises privacy concerns. Consequently, scholars have pursued formal privacy guarantees that limit the information a trained model can reveal about any single record.

Differential Privacy Overview

Differential privacy, the more established of the two frameworks, adds calibrated noise to either the training data or the model parameters. This stochastic perturbation ensures that the inclusion or exclusion of any single data point does not substantially change the output distribution, thereby providing a mathematically provable privacy bound.

PAC Privacy Overview

PAC (Probably Approximately Correct) privacy, a newer concept, frames privacy guarantees in terms of learning theory. Instead of focusing on output distributions, PAC privacy quantifies the probability that an adversary can correctly infer specific attributes of the training data, offering a complementary perspective to differential privacy.

Methodology and Datasets

The authors evaluated both privacy mechanisms on three publicly available datasets spanning healthcare, finance, and social science domains. Each dataset was split into training and testing partitions, and identical hyperparameter settings were applied to ensure a fair comparison. The study measured standard regression metrics such as mean squared error (MSE) alongside privacy loss parameters.

Key Findings

Results indicate that differential privacy generally incurs higher MSE penalties at comparable privacy levels, whereas PAC privacy can achieve similar predictive performance with reduced noise injection. However, the PAC approach exhibited greater sensitivity to dataset size, performing best on larger samples. The authors also note that the choice of privacy parameter critically influences the trade‑off between utility and confidentiality for both methods.

Implications for Practitioners

Practitioners seeking to deploy privacy‑preserving regression models may consider PAC privacy when data volume permits, as it can deliver higher accuracy without sacrificing formal privacy guarantees. Conversely, organizations requiring a well‑understood, regulatory‑compliant framework may favor differential privacy despite its performance cost.

Future Directions

The paper suggests extending the comparative analysis to other machine‑learning algorithms and exploring hybrid schemes that combine elements of both privacy paradigms. Further empirical work on diverse data distributions could refine guidance for real‑world deployments.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.