{"type":"ScholarlyArticle","title":"Hawkes Process Based on Controlled Differential Equations","authors":[{"name":"Minju Jo","slug":"minju-jo","given":"Minju","family":"Jo","affiliation":"Yonsei University , Seoul , South Korea"},{"name":"Seungji Kook","slug":"seungji-kook","given":"Seungji","family":"Kook","affiliation":"Yonsei University , Seoul , South Korea"},{"name":"Noseong Park","slug":"noseong-park","given":"Noseong","family":"Park","affiliation":"Yonsei University , Seoul , South Korea"}],"abstract":"Hawkes processes are a popular framework to model the occurrence of sequential events, i.e., occurrence dynamics, in several fields such as social diffusion. In real-world scenarios, the inter-arrival time among events is irregular. However, existing neural network-based Hawkes process models not only i) fail to capture such complicated irregular dynamics, but also ii) resort to heuristics to calculate the log-likelihood of events since they are mostly based on neural networks designed for regular discrete inputs. To this end, we present the concept of Hawkes process based on controlled differential equations (HP-CDE), by adopting the neural controlled differential equation (neural CDE) technology which is an analogue to continuous RNNs. Since HP-CDE continuously reads data, i) irregular time-series datasets can be properly treated preserving their uneven temporal spaces, and ii) the log-likelihood can be exactly computed. Moreover, as both Hawkes processes and neural CDEs are first developed to model complicated human behavioral dynamics, neural CDE-based Hawkes processes are successful in modeling such occurrence dynamics. In our experiments with 4 real-world datasets, our method outperforms existing methods by non-trivial margins.","doi":"10.24963/ijcai.2023/239","url":"https://ijcai.org/proceedings/2023/239","pdf":"https://ijcai.org/proceedings/2023/0239.pdf","markdown":"https://ijcai.org/proceedings/2023/239.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/239","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Data Mining","track":"Main Track","number":239,"pages":{"first":2151,"last":2159},"keywords":["Data Mining: DM: Mining spatial and/or temporal data","Data Mining: DM: Mining text, web, social media"],"videos":[],"references":[{"position":1,"raw":"[Aitchison and Silvey, 1958] J. 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