Black-box Variational Inference for Stochastic Differential Equations

TL;DR

This paper introduces a black-box variational inference method for stochastic differential equations that jointly estimates parameters and diffusion paths using neural networks, applicable to various SDE systems with minimal tuning.

Contribution

It proposes a novel neural network-based variational inference approach for SDEs, enabling efficient joint parameter and path inference with minimal tuning.

Findings

Accurate parameter estimates for Lotka-Volterra system

Effective inference on epidemic model

Applicable to diverse SDE systems

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.