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Bibliographic Details
Main Authors: Cao, Zilong, Bi, Xuan, Zhang, Hai
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2602.22282
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author Cao, Zilong
Bi, Xuan
Zhang, Hai
author_facet Cao, Zilong
Bi, Xuan
Zhang, Hai
contents Data privacy is important in the AI era, and differential privacy (DP) is one of the golden solutions. However, DP is typically applicable only if data have a bounded underlying distribution. We address this limitation by leveraging second-moment information from a small amount of public data. We propose Public-moment-guided Truncation (PMT), which transforms private data using the public second-moment matrix and applies a principled truncation whose radius depends only on non-private quantities: data dimension and sample size. This transformation yields a well-conditioned second-moment matrix, enabling its inversion with a significantly strengthened ability to resist the DP noise. Furthermore, we demonstrate the applicability of PMT by using penalized and generalized linear regressions. Specifically, we design new loss functions and algorithms, ensuring that solutions in the transformed space can be mapped back to the original domain. We have established improvements in the models' DP estimation through theoretical error bounds, robustness guarantees, and convergence results, attributing the gains to the conditioning effect of PMT. Experiments on synthetic and real datasets confirm that PMT substantially improves the accuracy and stability of DP models.
format Preprint
id arxiv_https___arxiv_org_abs_2602_22282
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Differentially Private Truncation of Unbounded Data via Public Second Moments
Cao, Zilong
Bi, Xuan
Zhang, Hai
Cryptography and Security
Machine Learning
Applications
Methodology
Primary 62F30, secondary 62J05, 62J12, 62G20, 68P27
G.3; G.1.6; K.4.1; I.5.1
Data privacy is important in the AI era, and differential privacy (DP) is one of the golden solutions. However, DP is typically applicable only if data have a bounded underlying distribution. We address this limitation by leveraging second-moment information from a small amount of public data. We propose Public-moment-guided Truncation (PMT), which transforms private data using the public second-moment matrix and applies a principled truncation whose radius depends only on non-private quantities: data dimension and sample size. This transformation yields a well-conditioned second-moment matrix, enabling its inversion with a significantly strengthened ability to resist the DP noise. Furthermore, we demonstrate the applicability of PMT by using penalized and generalized linear regressions. Specifically, we design new loss functions and algorithms, ensuring that solutions in the transformed space can be mapped back to the original domain. We have established improvements in the models' DP estimation through theoretical error bounds, robustness guarantees, and convergence results, attributing the gains to the conditioning effect of PMT. Experiments on synthetic and real datasets confirm that PMT substantially improves the accuracy and stability of DP models.
title Differentially Private Truncation of Unbounded Data via Public Second Moments
topic Cryptography and Security
Machine Learning
Applications
Methodology
Primary 62F30, secondary 62J05, 62J12, 62G20, 68P27
G.3; G.1.6; K.4.1; I.5.1
url https://arxiv.org/abs/2602.22282