# Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels

arXiv: https://arxiv.org/abs/2104.01029 · HTML: https://mlsanity.com/paper/2104.01029/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 2 Apr 2021.

## Builds on (most cited first, 14 of 14)

- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Expecting to be HIP: Hawkes Intensity Processes for Social Media Popularity](https://mlsanity.com/paper/1602.06033/) (2016)
- [Shaping Social Activity by Incentivizing Users](https://mlsanity.com/paper/1408.0406/) (2014)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Learning Hawkes Processes from a Handful of Events](https://mlsanity.com/paper/1911.00292/) (2019)
- [The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks](https://mlsanity.com/paper/1711.10967/) (2017)
- [HypTrails: A Bayesian Approach for Comparing Hypotheses About Human Trails on the Web](https://mlsanity.com/paper/1411.2844/) (2014)
- [Distilling Information Reliability and Source Trustworthiness from Digital Traces](https://mlsanity.com/paper/1610.07472/) (2016)
- [Modeling Interdependent and Periodic Real-World Action Sequences](https://mlsanity.com/paper/1802.09148/) (2018)
- [Fast Estimation of Causal Interactions using Wold Processes](https://mlsanity.com/paper/1807.04595/) (2018)
- [Mean-field inference of Hawkes point processes](https://mlsanity.com/paper/1511.01512/) (2015)
- [HNP3: A Hierarchical Nonparametric Point Process for Modeling Content Diffusion over Social Media](https://mlsanity.com/paper/1610.00246/) (2016)
- [Discovering Topical Interactions in Text-based Cascades using Hidden Markov Hawkes Processes](https://mlsanity.com/paper/1809.04487/) (2018)
- [Uncovering the Dynamics of Crowdlearning and the Value of Knowledge](https://mlsanity.com/paper/1612.04831/) (2016)

## Built on by (most cited first, 2 of 2)

- [A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks](https://mlsanity.com/paper/2205.09263/) (2022)
- [The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks](https://mlsanity.com/paper/2205.00639/) (2022)

## Abstract (arXiv)

As a tool for capturing irregular temporal dependencies (rather than resorting to binning temporal observations to construct time series), Hawkes processes with exponential decay have seen widespread adoption across many application domains, such as predicting the occurrence time of the next earthquake or stock market spike. However, practical applications of Hawkes processes face a noteworthy challenge: There is substantial and often unquantified variance in decay parameter estimations, especially in the case of a small number of observations or when the dynamics behind the observed data suddenly change. We empirically study the cause of these practical challenges and we develop an approach to surface and thereby mitigate them. In particular, our inspections of the Hawkes process likelihood function uncover the properties of the uncertainty when fitting the decay parameter. We thus propose to explicitly capture this uncertainty within a Bayesian framework. With a series of experiments with synthetic and real-world data from domains such as "classical" earthquake modeling or the manifestation of collective emotions on Twitter, we demonstrate that our proposed approach helps to quantify uncertainty and thereby to understand and fit Hawkes processes in practice.