Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels
This work addresses a practical challenge for users of Hawkes processes in domains such as seismology and social media, but it is incremental as it builds on existing Bayesian frameworks to handle estimation uncertainty.
The paper tackles the problem of unquantified variance in decay parameter estimations of Hawkes processes with exponential kernels, especially with limited or changing data, by developing a Bayesian approach to surface and mitigate this uncertainty. The result is a method that helps quantify uncertainty and improve the understanding and fitting of Hawkes processes in practical applications like earthquake modeling and Twitter emotion analysis.
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.