Time Changed Normalizing Flows for Accurate SDE Modeling

The generative paradigm has become increasingly important in machine learning and deep slearning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a base distribution through diffeomorphic transformations. Extending the normalizin...

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Bibliographic Details
Published inICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 6395 - 6399
Main Authors Bekri, Naoufal El, Drumetz, Lucas, Vermet, Franck
Format Conference Proceeding
LanguageEnglish
Published IEEE 14.04.2024
Subjects
convex neural network
deep generative models
Dynamics
Estimation
Gaussian processes
Mathematical models
normalizing flows
Predictive models
Stochastic differential equations
time series
Time series analysis
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Summary:The generative paradigm has become increasingly important in machine learning and deep slearning 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 provided 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, generalizes prior methodologies, and leads to improved results and better inference and prediction capability.
ISSN:2379-190X
DOI:10.1109/ICASSP48485.2024.10446131