Differentially Private Learning of Hawkes Processes
This work addresses privacy concerns in modeling event sequence data, offering incremental improvements by analyzing sample complexity for differentially private Hawkes processes.
The paper tackles the problem of learning Hawkes processes with differential privacy, providing both non-private and private estimators for parameters μ and α, and quantifying the sample complexity cost of privacy.
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 $μ$ and excitation function $αe^{-βt}$. We provide both non-private and differentially private estimators of $μ$ and $α$, 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.