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Identifying Latent Stochastic Differential Equations

Publication ,  Journal Article
Hasan, A; Pereira, JM; Farsiu, S; Tarokh, V
Published in: IEEE Transactions on Signal Processing
January 1, 2022

We present a method for learning latent stochastic differential equations (SDEs) from high dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown Itô process, the proposed method learns the mapping from ambient to latent space, and the underlying SDE coefficients, through a self-supervised learning approach. Using the framework of variational autoencoders, we consider a conditional generative model for the data based on the Euler-Maruyama approximation of SDE solutions. Furthermore, we use recent results on identifiability of latent variable models to show that the proposed model can recover not only the underlying SDE coefficients, but also the original latent variables, up to an isometry, in the limit of infinite data. We validate the method through several simulated video processing tasks, where the underlying SDE is known, and through real world datasets.

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Published In

IEEE Transactions on Signal Processing

DOI

EISSN

1941-0476

ISSN

1053-587X

Publication Date

January 1, 2022

Volume

70

Start / End Page

89 / 104

Related Subject Headings

  • Networking & Telecommunications
 

Citation

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Hasan, A., Pereira, J. M., Farsiu, S., & Tarokh, V. (2022). Identifying Latent Stochastic Differential Equations. IEEE Transactions on Signal Processing, 70, 89–104. https://doi.org/10.1109/TSP.2021.3131723
Hasan, A., J. M. Pereira, S. Farsiu, and V. Tarokh. “Identifying Latent Stochastic Differential Equations.” IEEE Transactions on Signal Processing 70 (January 1, 2022): 89–104. https://doi.org/10.1109/TSP.2021.3131723.
Hasan A, Pereira JM, Farsiu S, Tarokh V. Identifying Latent Stochastic Differential Equations. IEEE Transactions on Signal Processing. 2022 Jan 1;70:89–104.
Hasan, A., et al. “Identifying Latent Stochastic Differential Equations.” IEEE Transactions on Signal Processing, vol. 70, Jan. 2022, pp. 89–104. Scopus, doi:10.1109/TSP.2021.3131723.
Hasan A, Pereira JM, Farsiu S, Tarokh V. Identifying Latent Stochastic Differential Equations. IEEE Transactions on Signal Processing. 2022 Jan 1;70:89–104.

Published In

IEEE Transactions on Signal Processing

DOI

EISSN

1941-0476

ISSN

1053-587X

Publication Date

January 1, 2022

Volume

70

Start / End Page

89 / 104

Related Subject Headings

  • Networking & Telecommunications