Neural Jump Stochastic Differential Equations
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Many time series can be effectively modeled with a combination of continuous flows along with random jumps sparked by discrete 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 stochastic events cause an abrupt change in the latent variables. 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, medical records, awards on Stack Overflow, and earthquake monitoring.
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