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Online Learning for Multivariate Hawkes Processes
Yingxiang Yang · Jalal Etesami · Niao He · Negar Kiyavash

Wed Dec 06 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #49 #None
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.

Author Information

Yingxiang Yang (University of Illinois at Urbana Champaign)
Jalal Etesami (UIUC)
Niao He (UIUC)
Negar Kiyavash (Georgia Tech)

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