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 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 as the conditioned diffusion process does. The resulting black-box 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.