Identifying Latent Stochastic Differential Equations

• URL: http://arxiv.org/abs/2007.06075v5
• Date: Fri, 26 Nov 2021 23:41:49 GMT
• Title: Identifying Latent Stochastic Differential Equations
• Authors: Ali Hasan, Jo\~ao M. Pereira, Sina Farsiu, Vahid Tarokh
• Abstract summary: We present a method for learning latent differential equations (SDEs) from high-dimensional time series data. The proposed method learns the mapping from ambient to latent space, and the underlying SDE coefficients, through a self-supervised learning approach. We validate the method through several simulated video processing tasks, where the underlying SDE is known, and through real world datasets.
• Score: 29.103393300261587
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 It\^o 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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