{"type":"ScholarlyArticle","title":"Efficient Non-parametric Bayesian Hawkes Processes","authors":[{"name":"Rui Zhang","slug":"rui-zhang","given":"Rui","family":"Zhang","affiliation":"The Australian National University , Australia; Data61 CSIRO , Australia"},{"name":"Christian Walder","slug":"christian-walder","given":"Christian","family":"Walder","affiliation":"The Australian National University , Australia; Data61 CSIRO , Australia"},{"name":"Marian-Andrei Rizoiu","slug":"marian-andrei-rizoiu","given":"Marian-Andrei","family":"Rizoiu","affiliation":"University of Technology Sydney , Australia"},{"name":"Lexing Xie","slug":"lexing-xie","given":"Lexing","family":"Xie","affiliation":"The Australian National University , Australia; Data61 CSIRO , Australia"}],"abstract":"In this paper, we develop an efficient non-parametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the stationarity of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms --- a block Gibbs sampler and a maximum a posteriori estimator based on expectation maximization --- and we show that our methods have a linear time complexity, both theoretically and empirically. On synthetic data, we show our methods to be able to infer flexible Hawkes triggering kernels. On two large-scale Twitter diffusion datasets, we show that our methods outperform the current state-of-the-art in goodness-of-fit and that the time complexity is linear in the size of the dataset. We also observe that on diffusions related to online videos, the learned kernels reflect the perceived longevity for different content types such as music or pets videos.","doi":"10.24963/ijcai.2019/597","url":"https://ijcai.org/proceedings/2019/597","pdf":"https://ijcai.org/proceedings/2019/0597.pdf","markdown":"https://ijcai.org/proceedings/2019/597.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/597","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Machine Learning M-Z","track":"Main track","number":597,"pages":{"first":4299,"last":4305},"keywords":["Machine Learning: Time-series;Data Streams","Machine Learning: Learning Generative Models","Machine Learning: Probabilistic Machine Learning"],"videos":[],"references":[{"position":1,"raw":"[Adams et al., 2009] Ryan Prescott Adams, Iain Murray, and David J C MacKay. 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