title: 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.
authors: Ping Zhang Rishabh K Iyer Ashish V. Tendulkar Gaurav Aggarwal Abir De
hIndex: Rishabh K Iyer 18