Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation

• Published in: arXiv.org
• Main Authors: Brown, Gavin, Krishnamurthy Dvijotham, Evans, Georgina, Liu, Daogao, Smith, Adam, Thakurta, Abhradeep
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 21.02.2024
• Subjects: Algorithms; Confidence intervals; Empirical analysis; Statistical analysis; Synthetic data

We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time step. Our analysis leads to new results on the algorithm's...