  Stochastic differential equations (SDEs) have been widely used to model real
world random phenomena. Existing works mainly focus on the case where the time
series is modeled by a single SDE, which might be restrictive for modeling time
series with distributional shift. In this work, we propose a change point
detection algorithm for time series modeled as neural SDEs. Given a time series
dataset, the proposed method jointly learns the unknown change points and the
parameters of distinct neural SDE models corresponding to each change point.
Specifically, the SDEs are learned under the framework of generative
adversarial networks (GANs) and the change points are detected based on the
output of the GAN discriminator in a forward pass. At each step of the proposed
algorithm, the change points and the SDE model parameters are updated in an
alternating fashion. Numerical results on both synthetic and real datasets are
provided to validate the performance of our algorithm in comparison to
classical change point detection benchmarks, standard GAN-based neural SDEs,
and other state-of-the-art deep generative models for time series data.
