Locally Private Parametric Methods for Change-Point Detection

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 substantially improved finite-sample accuracy guarantees for a change-point detection algorithm based on the generalized log-likelihood ratio test, using martingale methods. In the private setting, we propose two locally differentially private algorithms based on randomized response and binary mechanisms, and analyze their performance across different privacy regimes, both theoretically and empirically. Our results characterize the statistical cost of local differential privacy in change-point detection and show how privacy constraints degrade performance relative to a non-private benchmark. As part of our analysis, we establish a structural result on strong data processing inequality (SDPI) coefficients for Jeffreys-Rényi divergence, which may also be of independent interest. We corroborate our theoretical results through empirical evaluation on synthetic data.