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Online Learning for Multivariate Hawkes Processes
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Authors: Yingxiang Yang,Jalal Etesami,Niao He,Negar Kiyavash
Where published: NeurIPS 2017 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/7079-online-learning-for-multivariate-hawkes-processes
We develop a nonparametric and online learning algorithm that estimates the triggering functions of a multivariate Hawkes process (MHP). The approach we take approximates the triggering function $f_{i,j}(t)$ by functions in a reproducing kernel Hilbert space (RKHS), and maximizes a time-discretized version of the log-likelihood, with Tikhonov regularization. Theoretically, our algorithm achieves an $\calO(\log T)$ regret bound. Numerical results show that our algorithm offers a competing performance to that of the nonparametric batch learning algorithm, with a run time comparable to the parametric online learning algorithm.
Where published: NeurIPS 2017 12
Document: PDF DOI
Abstract URL: http://papers.nips.cc/paper/7079-online-learning-for-multivariate-hawkes-processes
We develop a nonparametric and online learning algorithm that estimates the triggering functions of a multivariate Hawkes process (MHP). The approach we take approximates the triggering function $f_{i,j}(t)$ by functions in a reproducing kernel Hilbert space (RKHS), and maximizes a time-discretized version of the log-likelihood, with Tikhonov regularization. Theoretically, our algorithm achieves an $\calO(\log T)$ regret bound. Numerical results show that our algorithm offers a competing performance to that of the nonparametric batch learning algorithm, with a run time comparable to the parametric online learning algorithm.
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