Time-changed normalizing flows for accurate SDE modeling
This work addresses a specific limitation in generative modeling of stochastic processes for researchers in time series and SDE applications, representing an incremental advancement over prior dynamic normalizing flow methods.
The authors tackled the problem of modeling stochastic differential equations (SDEs) that cannot be effectively captured by existing dynamic normalizing flows, proposing Time Changed Normalizing Flows (TCNF) based on time deformation of Brownian motion, which improved inference and prediction capability for processes like the Ornstein-Uhlenbeck process.
The generative paradigm has become increasingly important in machine learning and deep learning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a base distribution through diffeomorphic transformations. Extending the normalizing flow framework to handle time-indexed flows gave dynamic normalizing flows, a powerful tool to model time series, stochastic processes, and neural stochastic differential equations (SDEs). In this work, we propose a novel variant of dynamic normalizing flows, a Time Changed Normalizing Flow (TCNF), based on time deformation of a Brownian motion which constitutes a versatile and extensive family of Gaussian processes. This approach enables us to effectively model some SDEs, that cannot be modeled otherwise, including standard ones such as the well-known Ornstein-Uhlenbeck process, and generalizes prior methodologies, leading to improved results and better inference and prediction capability.