Neural Stochastic Differential Equations with Bayesian Jumps for Marked Temporal Point Process (2019)

by Kazi Islam and Christian Shelton

Abstract: Many real-world systems evolve according to continuous dynamics and get interrupted by stochastic events i.e. systems that both flow (often described by a differential equation) and jump. If the equation of the continuous motion is unknown, the stochastic event generation process can be modeled as samples generated from a marked temporal point process, in the form of event sequences with non-uniform time intervals. Additionally, each event is marked with the type of the event and a real-valued noisy measurement. The noisy measurements themselves are the realizations of a stochastic process with an unknown stochastic differential equation (SDE). We present a framework that simultaneously models the intensity function of the temporal point process and learn stochastic process governing the distribution of the observed noisy measurements. Similar to the underlying system of interest, the latent dynamics of our framework evolves continuously according to ordinary differential equations (ODEs) while, the jumps at the observations are controlled by Gated Recurrent Units (GRUs) through a Bayesian update, which accounts for the observation noise. We present preliminary data fitting results on a real-world medical dataset.

Download Information

Kazi Islam and Christian Shelton (2019). "Neural Stochastic Differential Equations with Bayesian Jumps for Marked Temporal Point Process." NeurIPS workshop on Learning wtih Temporal Point Processes.

Bibtex citation

@inproceedings{IslShe19,
     author = "Kazi Islam and Christian Shelton",
     title = "Neural Stochastic Differential Equations with Bayesian Jumps for Marked Temporal Point Process",
     booktitle = "NeurIPS workshop on Learning wtih Temporal Point Processes",
     year = 2019
}

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