Abstract
In this paper, we address the problem of fitting multivariate Hawkes processes to potentially large-scale data in a setting where series of events are not only mutually-exciting but can also exhibit inhibitive patterns. We focus on nonparametric learning and propose a novel algorithm called MEMIP (Markovian Estimation of Mutually Interacting Processes) that makes use of polynomial approximation theory and self-concordant analysis in order to learn both triggering kernels and base intensities of events. Moreover, considering that N historical observations are available, the algorithm performs log-likelihood maximization in O(N) operations, while the complexity of non-Markovian methods is in O(N 2). Numerical experiments on simulated data, as well as real-world data, show that our method enjoys improved prediction performance when compared to state-of-the art methods like MMEL and exponential kernels.
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Lemonnier, R., Vayatis, N. (2014). Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes. In: Calders, T., Esposito, F., Hüllermeier, E., Meo, R. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2014. Lecture Notes in Computer Science(), vol 8725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44851-9_11
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DOI: https://doi.org/10.1007/978-3-662-44851-9_11
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