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Poster

Online Learning for Multivariate Hawkes Processes

Yingxiang Yang · Jalal Etesami · Niao He · Negar Kiyavash

Pacific Ballroom #49

Keywords: [ Online Learning ] [ Time Series Analysis ]


Abstract: 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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