Learning to Select Exogenous Events for Marked Temporal Point Process

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.