  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.
