Differentially Private Learning of Hawkes Processes

TL;DR

This paper analyzes the sample complexity of learning and privately releasing parameters of Hawkes processes, providing estimators and theoretical bounds, validated on synthetic and real data.

Contribution

It introduces differentially private estimators for Hawkes process parameters and derives sample complexity bounds, advancing understanding of privacy costs in this context.

Findings

Derived sample complexity bounds for non-private estimation.

Established privacy-preserving estimation methods with quantifiable costs.

Validated theoretical results on synthetic and real datasets.

Abstract

Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as sample complexity for learning the parameters and releasing differentially private versions, are yet to be thoroughly analyzed. In this work, we study standard Hawkes processes with background intensity $\mu$ and excitation function $\alpha e^{-\beta t}$. We provide both non-private and differentially private estimators of $\mu$ and $\alpha$, and obtain sample complexity results in both settings to quantify the cost of privacy. Our analysis exploits the strong mixing property of Hawkes processes and classical central limit theorem results for weakly dependent random variables. We validate our theoretical findings on both synthetic and real datasets.