Black-box Variational Inference for Stochastic Differential Equations

Code

• github.com/Tom-Ryder/VIforSDEs
  OfficialIn papertf★ 0
• github.com/anonmaths/tumour_sde_model
  tf★ 0

Abstract

Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an Euler-Maruyama discretisation for the diffusion, we use variational inference to jointly learn the parameters and the diffusion paths. We use a standard mean-field 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 black-box inference method can be applied to any SDE system with light tuning requirements. We illustrate the method on a Lotka-Volterra system and an epidemic model, producing accurate parameter estimates in a few hours.

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Reproductions