Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

dc.contributor.authorMalem-Shinitski, Noa
dc.contributor.authorOjeda, César
dc.contributor.authorOpper, Manfred
dc.date.accessioned2022-04-01T11:15:27Z
dc.date.available2022-04-01T11:15:27Z
dc.date.issued2022-02-28
dc.date.updated2022-03-23T07:36:52Z
dc.description.abstractTraditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.en
dc.description.sponsorshipDFG, 318763901, SFB 1294: Datenassimilation – Die nahtlose Verschmelzung von Daten und Modellenen
dc.description.sponsorshipBMBF, 01IS18025A, Verbundprojekt BIFOLD-BBDC: Berlin Institute for the Foundations of Learning and Dataen
dc.description.sponsorshipBMBF, 01IS18037A, Verbundprojekt BIFOLD-BZML: Berlin Institute for the Foundations of Learning and Dataen
dc.identifier.eissn1099-4300
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/16664
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15441
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.otherBayesian inferenceen
dc.subject.otherpoint processen
dc.subject.otherGaussian processen
dc.titleVariational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effectsen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber356en
dcterms.bibliographicCitation.doi10.3390/e24030356en
dcterms.bibliographicCitation.issue3en
dcterms.bibliographicCitation.journaltitleEntropyen
dcterms.bibliographicCitation.originalpublishernameMDPIen
dcterms.bibliographicCitation.originalpublisherplaceBaselen
dcterms.bibliographicCitation.volume24en
tub.accessrights.dnbfreeen
tub.affiliationFak. 4 Elektrotechnik und Informatik::Inst. Softwaretechnik und Theoretische Informatik::FG Methoden der Künstlichen Intelligenzde
tub.affiliation.facultyFak. 4 Elektrotechnik und Informatikde
tub.affiliation.groupFG Methoden der Künstlichen Intelligenzde
tub.affiliation.instituteInst. Softwaretechnik und Theoretische Informatikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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