Differentiable Bayesian inference of SDE parameters using a pathwise series expansion of Brownian motion

Sanmitra Ghosh, Paul J. Birrell, Daniela De Angelis
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:10982-10998, 2022.

Abstract

By invoking a pathwise series expansion of Brownian motion, we propose to approximate a stochastic differential equation (SDE) with an ordinary differential equation (ODE). This allows us to reformulate Bayesian inference for a SDE as the parameter estimation task for an ODE. Unlike a nonlinear SDE, the likelihood for an ODE model is tractable and its gradient can be obtained using adjoint sensitivity analysis. This reformulation allows us to use an efficient sampler, such as NUTS, that rely on the gradient of the log posterior. Applying the reparameterisation trick, variational inference can also be used for the same estimation task. We illustrate the proposed method on a variety of SDE models. We obtain similar parameter estimates when compared to data augmentation techniques.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-ghosh22a, title = { Differentiable Bayesian inference of SDE parameters using a pathwise series expansion of Brownian motion }, author = {Ghosh, Sanmitra and Birrell, Paul J. and De Angelis, Daniela}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {10982--10998}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/ghosh22a/ghosh22a.pdf}, url = {https://proceedings.mlr.press/v151/ghosh22a.html}, abstract = { By invoking a pathwise series expansion of Brownian motion, we propose to approximate a stochastic differential equation (SDE) with an ordinary differential equation (ODE). This allows us to reformulate Bayesian inference for a SDE as the parameter estimation task for an ODE. Unlike a nonlinear SDE, the likelihood for an ODE model is tractable and its gradient can be obtained using adjoint sensitivity analysis. This reformulation allows us to use an efficient sampler, such as NUTS, that rely on the gradient of the log posterior. Applying the reparameterisation trick, variational inference can also be used for the same estimation task. We illustrate the proposed method on a variety of SDE models. We obtain similar parameter estimates when compared to data augmentation techniques. } }
Endnote
%0 Conference Paper %T Differentiable Bayesian inference of SDE parameters using a pathwise series expansion of Brownian motion %A Sanmitra Ghosh %A Paul J. Birrell %A Daniela De Angelis %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-ghosh22a %I PMLR %P 10982--10998 %U https://proceedings.mlr.press/v151/ghosh22a.html %V 151 %X By invoking a pathwise series expansion of Brownian motion, we propose to approximate a stochastic differential equation (SDE) with an ordinary differential equation (ODE). This allows us to reformulate Bayesian inference for a SDE as the parameter estimation task for an ODE. Unlike a nonlinear SDE, the likelihood for an ODE model is tractable and its gradient can be obtained using adjoint sensitivity analysis. This reformulation allows us to use an efficient sampler, such as NUTS, that rely on the gradient of the log posterior. Applying the reparameterisation trick, variational inference can also be used for the same estimation task. We illustrate the proposed method on a variety of SDE models. We obtain similar parameter estimates when compared to data augmentation techniques.
APA
Ghosh, S., Birrell, P.J. & De Angelis, D.. (2022). Differentiable Bayesian inference of SDE parameters using a pathwise series expansion of Brownian motion . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:10982-10998 Available from https://proceedings.mlr.press/v151/ghosh22a.html.

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