Variational Neural Stochastic Differential Equations with Change Points
This work addresses the problem of detecting distribution shifts in time-series data for applications in fields like finance or healthcare, but it appears incremental as it builds on existing neural SDE and VAE frameworks.
The authors tackled modeling change points in time-series data using neural stochastic differential equations (neural SDEs) by proposing a novel variational autoencoder-based formulation and training procedure, which effectively modeled both classical parametric SDEs and real datasets with distribution shifts.
In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE) framework for modeling time-series as a neural SDE. Unlike existing algorithms training neural SDEs as VAEs, our proposed algorithm only necessitates a Gaussian prior of the initial state of the latent stochastic process, rather than a Wiener process prior on the entire latent stochastic process. We develop two methodologies for modeling and estimating change points in time-series data with distribution shifts. Our iterative algorithm alternates between updating neural SDE parameters and updating the change points based on either a maximum likelihood-based approach or a change point detection algorithm using the sequential likelihood ratio test. We provide a theoretical analysis of this proposed change point detection scheme. Finally, we present an empirical evaluation that demonstrates the expressive power of our proposed model, showing that it can effectively model both classical parametric SDEs and some real datasets with distribution shifts.