Black-Box Variational Inference for Stochastic Differential Equations

Tom Ryder, Andrew Golightly, A. Stephen McGough, Dennis Prangle
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4423-4432, 2018.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-ryder18a, title = {Black-Box Variational Inference for Stochastic Differential Equations}, author = {Ryder, Tom and Golightly, Andrew and McGough, A. Stephen and Prangle, Dennis}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {4423--4432}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/ryder18a/ryder18a.pdf}, url = {https://proceedings.mlr.press/v80/ryder18a.html}, 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.} }
Endnote
%0 Conference Paper %T Black-Box Variational Inference for Stochastic Differential Equations %A Tom Ryder %A Andrew Golightly %A A. Stephen McGough %A Dennis Prangle %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-ryder18a %I PMLR %P 4423--4432 %U https://proceedings.mlr.press/v80/ryder18a.html %V 80 %X 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.
APA
Ryder, T., Golightly, A., McGough, A.S. & Prangle, D.. (2018). Black-Box Variational Inference for Stochastic Differential Equations. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:4423-4432 Available from https://proceedings.mlr.press/v80/ryder18a.html.

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