Hawkesian Graphical Event Models

Abstract

Graphical event models (GEMs) provide a framework for graphical representation of multivariate point processes. We propose a class of GEMs named Hawkesian graphical event models (HGEMs) for representing temporal dependencies among different types of events from either a single event stream or multiple independent streams. In our proposed model, the intensity function for an event label is a linear combination of time-shifted kernels where time shifts correspond to prior occurrences of causal event labels in the history, as in a Hawkes process. The number of parameters in our model scales linearly in the number of edges in the graphical model, enabling efficient estimation and inference. This is in contrast to many existing GEMs where the number of parameters scales exponentially in the edges. We use two types of kernels: exponential and Gaussian kernels, and propose a two-step algorithm that combines the strengths of both kernels and learns the structure for the underlying graphical model. Experiments on both synthetic and real-world data demonstrate the efficacy of the proposed HGEM, and exhibit expressive power of the two-step learning algorithm in characterizing self-exciting event patterns and reflecting intrinsic Granger-causal relationships.