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Statistical Inference for Differentially Private Stochastic Gradient Descent

Published: July 28, 2025 | arXiv ID: 2507.20560v1

By: Xintao Xia, Linjun Zhang, Zhanrui Cai

Potential Business Impact:

Makes private data safe for computer learning.

Business Areas:
Predictive Analytics Artificial Intelligence, Data and Analytics, Software

Privacy preservation in machine learning, particularly through Differentially Private Stochastic Gradient Descent (DP-SGD), is critical for sensitive data analysis. However, existing statistical inference methods for SGD predominantly focus on cyclic subsampling, while DP-SGD requires randomized subsampling. This paper first bridges this gap by establishing the asymptotic properties of SGD under the randomized rule and extending these results to DP-SGD. For the output of DP-SGD, we show that the asymptotic variance decomposes into statistical, sampling, and privacy-induced components. Two methods are proposed for constructing valid confidence intervals: the plug-in method and the random scaling method. We also perform extensive numerical analysis, which shows that the proposed confidence intervals achieve nominal coverage rates while maintaining privacy.

Page Count
35 pages

Category
Statistics:
Machine Learning (Stat)