Black-box Variational Inference for Stochastic Differential Equations

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.

arXiv commentV3 - revised based on ICML reviewer comments V2 - added acknowledgements and link to code

References in corpus (8)

• Auto-Encoding Variational Bayes
• Stochastic Backpropagation and Approximate Inference in Deep Generative Models
• Variational Inference with Normalizing Flows
• Pareto Smoothed Importance Sampling
• Black box variational inference for state space models
• Inference for SDE models via Approximate Bayesian Computation
• Gaussian variational approximation for high-dimensional state space models
• Automatic Variational ABC

Cited by in corpus (9)

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• Scalable Gradients for Stochastic Differential Equations
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• Stochastic Normalizing Flows
• Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations
• Differential Bayesian Neural Nets
• Learning Continuous-Time Dynamics by Stochastic Differential Networks
• Variational bridge constructs for approximate Gaussian process regression