We study parametric change-point detection, where the goal is to identify distributional changes in time series, under local differential privacy. In the non-private setting, we derive improved finite-sample accuracy guarantees for a change-point detection algorithm based on the generalized log-likelihood ratio test, via martingale methods. In the private setting, we propose two locally differentially private algorithms based on randomized response and binary mechanisms, and analyze their theoretical performance. We derive bounds on detection accuracy and validate our results through empirical evaluation. Our results characterize the statistical cost of local differential privacy in change-point detection and show how privacy degrades performance relative to a non-private benchmark. As part of this analysis, we establish a structural result for strong data processing inequalities (SDPI), proving that SDPI coefficients for Rényi divergences and their symmetric variants (Jeffreys-Rényi divergences) are achieved by binary input distributions. These results on SDPI coefficients are also of independent interest, with applications to statistical estimation, data compression, and Markov chain mixing.

翻译：本文研究局部差分隐私下的参数化变点检测问题，其目标是在时间序列中识别分布变化。在非隐私设定下，我们通过鞅方法为基于广义对数似然比检验的变点检测算法推导出改进的有限样本精度保证。在隐私设定下，我们提出两种基于随机响应与二元机制的局部差分隐私算法，并分析其理论性能。我们推导了检测精度的边界，并通过实证评估验证了结果。我们的研究结果刻画了局部差分隐私在变点检测中的统计代价，揭示了隐私保护相对于非隐私基准的性能衰减机制。作为分析的一部分，我们建立了强数据处理不等式（SDPI）的结构性结论，证明了Rényi散度及其对称变体（Jeffreys-Rényi散度）的SDPI系数可通过二元输入分布实现。这些关于SDPI系数的结论本身也具有独立价值，可应用于统计估计、数据压缩和马尔可夫链混合分析等领域。