在局部差分隐私下实现时间序列变化点检测，分析隐私对性能的影响。
Locally Private Parametric Methods for Change-Point Detection
- 基于广义似然比检验，结合鞅方法提升非私有场景下的检测精度
- 提出两种基于随机响应与二元机制的本地差分隐私算法，理论证明其检测误差上界
- 揭示隐私保护带来的统计代价，适用于关注数据隐私的时序分析研究者
我们研究在局部差分隐私约束下进行参数化变化点检测的问题，目标是识别时间序列中的分布变化。在非私有设置下，通过鞅方法推导出基于广义对数似然比检验的算法在有限样本下的改进精度保证。在私有设置下，提出了两种基于随机响应和二元机制的本地差分隐私算法，并分析了其理论性能。我们给出了检测准确性的上界，并通过实证评估验证了结果。研究结果刻画了局部差分隐私在变化点检测中的统计代价，揭示了隐私保护如何降低性能相对于非私有基准。作为分析的一部分，我们建立了强数据处理不等式（SDPI）的结构性结果，证明瑞尼散度及其对称变体（杰弗里斯-瑞尼散度）的SDPI系数在二元输入分布下达到极值。这些关于SDPI系数的结果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等领域。
原文摘要 · Abstract (English)
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.
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