本地差分隐私下的参数化变点检测方法

View PDF

Abstract:We study parametric change-point detection under local differential privacy, focusing on the offline localization of a single change point in a sequence of independent observations.~In the non-private setting, we derive improved finite-sample accuracy guarantees for a generalized likelihood-ratio estimator using martingale methods.~We establish finite-sample minimax lower bounds in both the non-private and locally private settings, showing that localization accuracy is fundamentally limited by the Chernoff information between the pre- and post-change distributions.~Guided by this, we design locally private CPD algorithms based on aggregated randomized response and binary mechanisms, which maximize the Chernoff information between the induced output distributions in low- and high-privacy regimes, respectively, and derive their finite-sample guarantees. Together, our upper and lower bounds quantify the statistical cost of privacy in change-point localization.~As part of our analysis, we also show that strong data processing inequality coefficients of Rényi divergence and Jeffreys--Rényi divergence of order infinity can be computed by restricting to pairs of input distributions with a common support of at most two symbols.~We corroborate our results through empirical evaluation on synthetic data.

Comments:	60 pages
Subjects:	Machine Learning (stat.ML); Information Theory (cs.IT); Machine Learning (cs.LG); Methodology (stat.ME)
Cite as:	arXiv:2602.13619 [stat.ML]
	(or arXiv:2602.13619v2 [stat.ML] for this version)
	https://doi.org/10.48550/arXiv.2602.13619 arXiv-issued DOI via DataCite

Submission history

From: Anuj Kumar Yadav [view email]
[v1] Sat, 14 Feb 2026 06:11:54 UTC (213 KB)
[v2] Fri, 9 Oct 2026 10:10:03 UTC (487 KB)