Forward sampling for State Variable Graphical Event Models with Markovian and piecewise constant dependencies

Graphical event models are dedicated to modelling continuous-time processes. Some of their extensions are used to represent event occurrences and state variable changes w.r.t time. But the existing models in the literature struggle to capture complex historical dependencies between variables, limiting their applications in real-world processes. To address this limitation, we define a new class of state variable graphical event models (SVGEMs) that deals with more complex piecewise constant historical dependencies. Sampling probabilistic graphical models is essential for approximate inference; previous studies have addressed this subject for several continuous-time models. However, sampling for graphical event models with various types of variables has not been explicitly described in the literature. To fill this gap, we also propose a forward sampling algorithm that unifies previous sampling algorithms into one single framework. A validation is performed with an experiment on randomly generated models, where we generate data using our sampling algorithm and show that the parameters of the models estimated from these data and priors converge to the ones of the underlying distribution. This work is the first one explicitly to describe a sampling algorithm for SVGEMs and pave the way for further research on the subject, including alternative SVGEM inference techniques such as importance sampling or Gibbs sampling.