Learning to Select Exogenous Events for Marked Temporal Point Process

Ping Zhang, Rishabh K Iyer, Ashish V. Tendulkar, Gaurav Aggarwal, Abir De

Keywords: Temporal point process, time series, event selection

TL;DR: It learns to select exogenous events from a set of events in the context of marked temporal point processes

Abstract:

Marked temporal point processes (MTPPs) have emerged as a powerful modeling
tool for a wide variety of applications which are characterized using discrete
events localized in continuous time. In this context, the events are of two types
endogenous events which occur due to the influence of the previous events and
exogenous events which occur due to the effect of the externalities. However, in
practice, the events do not come with endogenous or exogenous labels. To this
end, our goal in this paper is to identify the set of exogenous events from a set of
unlabelled events. To do so, we first formulate the parameter estimation problem
in conjunction with exogenous event set selection problem and show that this
problem is NP hard. Next, we prove that the underlying objective is a monotone
and \alpha-submodular set function, with respect to the candidate set of exogenous
events. Such a characterization subsequently allows us to use a stochastic greedy
algorithm which was originally proposed in~\cite{greedy}for submodular maximization.
However, we show that it also admits an approximation guarantee for maximizing
\alpha-submodular set function, even when the learning algorithm provides an imperfect
estimates of the trained parameters. Finally, our experiments with synthetic and
real data show that our method performs better than the existing approaches built
upon superposition of endogenous and exogenous MTPPs.

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Code: https://github.com/noilreed/TPP-Select