Fine-Grained $ε$-Margin Closed-Form Stabilization of Parametric Hawkes Processes
This work addresses parameter instability in event stream modeling for applications like finance or social networks, but it is incremental as it builds on existing MLE optimization.
The paper tackles the instability of Maximum Likelihood Estimation (MLE) in parametric Hawkes processes by introducing a stabilization procedure, which outperforms traditional methods across sequences of varying lengths.
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.