Stochastic Normalizing Flows

• URL: http://arxiv.org/abs/2002.09547v2
• Date: Tue, 25 Feb 2020 19:17:18 GMT
• Title: Stochastic Normalizing Flows
• Authors: Liam Hodgkinson, Chris van der Heide, Fred Roosta, Michael W. Mahoney
• Abstract summary: We introduce normalizing flows for maximum likelihood estimation and variational inference (VI) using differential equations (SDEs) Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabling efficient training of neural SDEs. These SDEs can be used for constructing efficient chains to sample from the underlying distribution of a given dataset.
• Score: 52.92110730286403
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabling efficient training of neural SDEs as random neural ordinary differential equations. These SDEs can be used for constructing efficient Markov chains to sample from the underlying distribution of a given dataset. Furthermore, by considering families of targeted SDEs with prescribed stationary distribution, we can apply VI to the optimization of hyperparameters in stochastic MCMC.

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