Learning to Select Exogenous Events for Marked Temporal Point Process

Marked temporal point processes (MTPPs) have emerged as a powerful modelingtool for a wide variety of applications which are characterized using discreteevents localized in continuous time. In this context, the events are of two typesendogenous events which occur due to the influence of the previous events andexogenous events which occur due to the effect of the externalities. However, inpractice, the events do not come with endogenous or exogenous labels. To thisend, our goal in this paper is to identify the set of exogenous events from a set ofunlabelled events. To do so, we first formulate the parameter estimation problemin conjunction with exogenous event set selection problem and show that thisproblem is NP hard. Next, we prove that the underlying objective is a monotoneand \alpha-submodular set function, with respect to the candidate set of exogenousevents. Such a characterization subsequently allows us to use a stochastic greedyalgorithm 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 imperfectestimates of the trained parameters. Finally, our experiments with synthetic andreal data show that our method performs better than the existing approaches builtupon superposition of endogenous and exogenous MTPPs.