Neural Jump Stochastic Differential Equations
This work addresses the challenge of modeling complex hybrid systems for applications such as event prediction in healthcare or seismology, representing an incremental advancement by extending Neural ODEs with stochastic jump terms.
The paper tackles the problem of modeling time series with both continuous flows and discrete jumps by introducing Neural Jump Stochastic Differential Equations, a data-driven method that learns hybrid dynamics and demonstrates predictive capabilities on synthetic and real-world datasets like Hawkes processes and medical records.
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.