Abstract
Hawkes processes with exponential kernels are a ubiquitous tool for modeling and predicting event times. However, estimating their decay parameter is challenging, and there is a remarkable variability among decay parameter estimates. Moreover, this variability increases substantially in cases of a small number of realizations of the process or due to sudden changes to a system under study, for example, in the presence of exogenous shocks. In this work, we demonstrate that these estimation difficulties relate to the noisy, non-convex shape of the Hawkes process' log-likelihood as a function of the decay. To address uncertainty in the estimates, we propose to use a Bayesian approach to learn more about likely decay values. We show that our approach alleviates the decay estimation problem across a range of experiments with synthetic and real-world data. With our work, we support researchers and practitioners in their applications of Hawkes processes in general and in their interpretation of Hawkes process parameters in particular.
Original language | English |
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Pages (from-to) | 223-240 |
Number of pages | 18 |
Journal | Intelligent Data Analysis |
Volume | 27 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2023 |
Keywords
- Bayesian inference
- decay rate
- Hawkes process
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Vision and Pattern Recognition
- Artificial Intelligence