Black-box Variational Inference for Stochastic Differential Equations
This provides a black-box inference method for SDE systems with light tuning requirements, addressing a challenging problem in computational statistics, though it is incremental as it builds on existing variational techniques.
The paper tackles parameter inference for stochastic differential equations by using variational inference with a recurrent neural network to approximate posterior distributions, achieving accurate parameter estimates in a few hours on tested models.
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.