Black-box Variational Inference for Stochastic Differential Equations

Understand

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.