Graph Convolutional Neural Networks based Marked Point Process

A point process is a collection of positional variables in a given space, while a marked point process (MPP) is basically a point process that measures some additional feature or value at each point. Existing applications such as financial market models and hospitalization models have demonstrated that MPPS are suitable for modeling random events with meaningful values. A big challenge is to study the relationship between different types of events, or how different types of markers affect each other. While Hawkes procedures are an effective and efficient way to model point processes with internal influences, inferential methods of intensity functions can be expensive, especially for multi-dimensional processes. Graph convolutional Network (GCN) is a powerful neural network designed to directly process graphs. A GCN-based model is presented to study potential patterns in the marking process and to predict the location of future events without estimating the Hawkes intensity function. A real data set of water pipe leakage and rupture records over the last 50 years was used in the experiment, modeled as a marker point process, where leakage and rupture are two marker forms. Experimental results on synthetic data sets and real water pipe data sets show that the proposed model is superior to recent state-of-the-art methods.