Personalized w-Event Privacy for Infinite Stream Estimation

In applications such as event monitoring, log analysis, and video querying, $w$-event privacy protects individual data within a sliding time window while supporting accurate stream statistics. Existing studies on infinite data streams mainly assume homogeneous privacy requirements for all users, which cannot capture user-specific privacy preferences. This paper studies personalized $w$-event privacy for private data stream estimation. We first design the Personalized Window Size Mechanism (PWSM), which supports personalized privacy requirements at each time slot. Based on PWSM, we propose Personalized Budget Distribution (PBD) and Personalized Budget Absorption (PBA) to estimate streaming statistics under $\boldsymbol{w}$-Event $\boldsymbol{\mathcal{E}}$ Personalized Differential Privacy (($\boldsymbol{w}$, $\boldsymbol{\mathcal{E}}$)-EPDP). PBD guarantees that the budget reserved for the next time step is no smaller than the budget consumed in the previous release, while PBA improves the current budget by absorbing unused budgets from the previous $k$ time slots and borrowing from the next $k$ time slots. We further develop Dynamic Personalized Budget Distribution (DPBD) and Dynamic Personalized Budget Absorption (DPBA), which allow users to dynamically adjust privacy requirements while satisfying $(\tau, \boldsymbol{w}_B, \boldsymbol{w}_F)$-Event $(\boldsymbol{\mathcal{E}}_B, \boldsymbol{\mathcal{E}}_F)$-Personalized Differential Privacy. We prove that all proposed methods achieve the corresponding personalized differential privacy guarantees and derive their error upper bounds. Experiments show that our methods reduce estimation error by at least $53.6\%$ compared with state-of-the-art algorithms.