Time-changed normalizing flows for accurate SDE modeling

• URL: http://arxiv.org/abs/2312.14698v2
• Date: Mon, 15 Jan 2024 21:12:03 GMT
• Title: Time-changed normalizing flows for accurate SDE modeling
• Authors: Naoufal El Bekri and Lucas Drumetz and Franck Vermet
• Abstract summary: We propose a novel transformation of dynamic normalizing flows, based on time deformation of a Brownian motion. This approach enables us to effectively model some SDEs, that cannot be modeled otherwise.
• Score: 5.402030962296633
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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