BlackBox Variational Inference for Stochastic Differential Equations
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:44234432, 2018.
Abstract
Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an EulerMaruyama discretisation for the diffusion, we use variational inference to jointly learn the parameters and the diffusion paths. We use a standard meanfield variational approximation of the parameter posterior, and introduce a recurrent neural network to approximate the posterior for the diffusion paths conditional on the parameters. This neural network learns how to provide Gaussian state transitions which bridge between observations in a very similar way to the conditioned diffusion process. The resulting blackbox inference method can be applied to any SDE system with light tuning requirements. We illustrate the method on a LotkaVolterra system and an epidemic model, producing accurate parameter estimates in a few hours.
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