# Fine-Grained ε-Margin Closed-Form Stabilization of Parametric Hawkes Processes

arXiv: https://arxiv.org/abs/2105.03800 · HTML: https://mlsanity.com/paper/2105.03800/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 8 May 2021.

## Builds on (most cited first, 12 of 12)

- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Self-Attentive Hawkes Processes](https://mlsanity.com/paper/1907.07561/) (2019)
- [Tick: a Python library for statistical learning, with a particular emphasis on time-dependent modelling](https://mlsanity.com/paper/1707.03003/) (2017)
- [SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model Diffusions in Finite Populations](https://mlsanity.com/paper/1711.01679/) (2017)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Efficient Non-parametric Bayesian Hawkes Processes](https://mlsanity.com/paper/1810.03730/) (2018)
- [Learning Hawkes Processes from a Handful of Events](https://mlsanity.com/paper/1911.00292/) (2019)
- [Uncertainty Quantification for Inferring Hawkes Networks](https://mlsanity.com/paper/2006.07506/) (2020)
- [Variational Inference for Sparse Gaussian Process Modulated Hawkes Process](https://mlsanity.com/paper/1905.10496/) (2019)

## Abstract (arXiv)

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.