Identifying Latent Stochastic Differential Equations

Autor:	Ali Hasan, Joao M. Pereira, Sina Farsiu, Vahid Tarokh
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	FOS: Computer and information sciences Computer Science::Machine Learning Computer Science - Machine Learning Statistics - Machine Learning Signal Processing Machine Learning (stat.ML) Electrical and Electronic Engineering Machine Learning (cs.LG)
Popis:	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. Comment: 20 pages, 8 figures, to be published in IEEE Transactions of Signal Processing
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e9d4e095e7220d12a47c60c190c1d46 http://arxiv.org/abs/2007.06075 Zobrazit plný text záznamu