  Hawkes Processes have undergone increasing popularity as default tools for
modeling self- and mutually exciting interactions of discrete events in
continuous-time event streams. A Maximum Likelihood Estimation (MLE)
unconstrained optimization procedure over parametrically assumed forms of the
triggering kernels of the corresponding intensity function are a widespread
cost-effective modeling strategy, particularly suitable for data with few
and/or short sequences. However, the MLE optimization lacks guarantees, except
for strong assumptions on the parameters of the triggering kernels, and may
lead to instability of the resulting parameters .In the present work, we show
how a simple stabilization procedure improves the performance of the MLE
optimization without these overly restrictive assumptions.This stabilized
version of the MLE is shown to outperform traditional methods over sequences of
several different lengths.
