Locally Private Parametric Methods for Change-Point Detection

TL;DR

This paper investigates the impact of local differential privacy on change-point detection in time series, proposing new algorithms and analyzing their theoretical and empirical performance to understand privacy-accuracy trade-offs.

Contribution

It introduces two locally differentially private algorithms for change-point detection and provides theoretical bounds and structural results on SDPI coefficients, advancing understanding of privacy effects.

Findings

Privacy degrades change-point detection accuracy compared to non-private methods.

Proposed algorithms achieve quantifiable bounds on detection performance under privacy constraints.

Structural results on SDPI coefficients for Rènyi divergences are established.

Abstract

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 R\'enyi divergences and their symmetric variants (Jeffreys-R\'enyi 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.