Supp1-3131723.pdf

Abstract

We present a method for learning latent stochastic differential equations (SDEs) from high dimensional time series data. Given a time series generated from a lower dimensional Ito process, the proposed method uncovers the relevant coefficients of the SDE 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 space, up to an isometry, in the limit of infinite data. We validate the model through a series of different simulated video processing tasks where the underlying SDE is known. Our results suggest that the proposed method effectively learns the underlying SDE, as predicted by the theory. The proposed theory and method provide a foundation for a variety of downstream applications.