Statistical Inference for Differentially Private Stochastic Gradient Descent

Fuente: arXiv
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Autores principales: Xia, Xintao, Zhang, Linjun, Cai, Zhanrui
Formato: Preprint
Publicado: 2025
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author Xia, Xintao
Zhang, Linjun
Cai, Zhanrui
author_facet Xia, Xintao
Zhang, Linjun
Cai, Zhanrui
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_20560
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Statistical Inference for Differentially Private Stochastic Gradient Descent
Xia, Xintao
Zhang, Linjun
Cai, Zhanrui
Machine Learning
Methodology
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.
title Statistical Inference for Differentially Private Stochastic Gradient Descent
topic Machine Learning
Methodology
url https://arxiv.org/abs/2507.20560