Affiliation:
1. Institute of Interactive Systems and Data Science, TU Graz, Graz, Austria
2. Faculty of Computer Science and Mathematics, University of Passau, Passau, Germany
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.
Subject
Artificial Intelligence,Computer Vision and Pattern Recognition,Theoretical Computer Science
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