Temporal point process is widely used for sequential data modeling. In this paper, we focus on the problem of modeling sequential event propagation in graph, such as retweeting by social network users, news transmitting between websites, etc. Given a collection of event propagation sequences, conventional point process model consider only the event history, i.e. embed event history into a vector, not the latent graph structure. We propose a Graph Biased Temporal Point Process (GBTPP) leveraging the structural information from graph representation learning, where the direct influence between nodes and indirect influence from event history is modeled respectively. Moreover, the learned node embedding vector is also integrated into the embedded event history as side information. Experiments on a synthetic dataset and two real-world datasets show the efficacy of our model compared to conventional methods and state-of-the-art.
The models surveyed include generalized Polya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas. IN contagious processes (e.g. measles, hijacking, etc.) the occurrence of events increases the probability of further events occurring in the near future. Also several series of events may interact with each other, for example one might consider notifications of some disease in a number of adjacent regions which would interact through infectives or carriers moving between the regions. In this paper we postulate a model for such processes and derive a general expression for the point spectral matrices. These theoretical spectra are useful for comparison with spectra estimated from data and thus provide a means of evaluating the fit of such a model in the manner of Bartlett (1963). The model studied was put forward in an earlier paper (Hawkes, 1971) but the solution was obtained only in special cases. In this paper an elegant solution is obtained for the. general case. Consider a stationary k-variate point process N(t), where Ni(t) represents the cumulative number of events in the ith process up to time t, with intensity vector X = of dN(t) dt and covariance density matrix Massachusetts Institute of Technology and the University of Washington Reactive point processes (RPPs) are a new statistical model designed for predicting discrete events in time, based on past history. RPPs were developed to handle an important problem within the domain of electrical grid reliability: short term prediction of electrical grid failures (“manhole events”), including outages, fires, explosions, and smoking manholes, which can cause threats to public safety and reliability of electrical service in cities. RPPs incorporate self-exciting, self-regulating, and saturating components. The self-excitement occurs as a result of a past event, which causes a temporary rise in vulnerability to future events. The self-regulation occurs as a result of an external inspection which temporarily lowers vulnerability to future events. RPPs can saturate when too many events or inspections occur close together, which ensures that the probability of an event stays within a realistic range. Two of the operational challenges for power companies are i) making continuous-time failure predictions, and ii) cost benefit analysis for decision making and proactive maintenance. RPPs are naturally suited for handling both of these challenges. We use the model to predict power-grid failures in Manhattan over a short term horizon, and use to provide a cost benefit analysis of different proactive maintenance programs. 