Neural Jump Stochastic Differential Equations

TL;DR

Neural Jump Stochastic Differential Equations provide a data-driven framework to model hybrid systems with continuous flows and discrete jumps, capturing complex temporal dynamics in various real-world datasets.

Contribution

The paper introduces Neural Jump SDEs, extending Neural ODEs with stochastic jump processes to learn hybrid continuous-discrete dynamics from data.

Findings

Effective modeling of synthetic and real-world point processes.

Improved prediction of event timings and types.

Versatile application across domains like healthcare and seismology.

Abstract

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they are affected by jumps. To this end, we introduce Neural Jump Stochastic Differential Equations that provide a data-driven approach to learn continuous and discrete dynamic behavior, i.e., hybrid systems that both flow and jump. Our approach extends the framework of Neural Ordinary Differential Equations with a stochastic process term that models discrete events. We then model temporal point processes with a piecewise-continuous latent trajectory, where the discontinuities are caused by stochastic events whose conditional intensity depends on the latent state. We demonstrate the predictive capabilities of our model on a range of synthetic and real-world marked point process datasets, including classical point processes (such as Hawkes processes), awards on Stack Overflow, medical records, and earthquake monitoring.