Variational inference for nonlinear ordinary differential equations

Sanmitra Ghosh, Paul Birrell, Daniela De Angelis
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2719-2727, 2021.

Abstract

We apply the reparameterisation trick to obtain a variational formulation of Bayesian inference in nonlinear ODE models. By invoking the linear noise approximation we also extend this variational formulation to a stochastic kinetic model. Our proposed inference method does not depend on any emulation of the ODE solution and only requires the extension of automatic differentiation to an ODE. We achieve this through a novel and holistic approach that uses both forward and adjoint sensitivity analysis techniques. Consequently, this approach can cater to both small and large ODE models efficiently. Upon benchmarking on some widely used mechanistic models, the proposed inference method produced a reliable approximation to the posterior distribution, with a significant reduction in execution time, in comparison to MCMC.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-ghosh21b, title = { Variational inference for nonlinear ordinary differential equations }, author = {Ghosh, Sanmitra and Birrell, Paul and De Angelis, Daniela}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {2719--2727}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/ghosh21b/ghosh21b.pdf}, url = {https://proceedings.mlr.press/v130/ghosh21b.html}, abstract = { We apply the reparameterisation trick to obtain a variational formulation of Bayesian inference in nonlinear ODE models. By invoking the linear noise approximation we also extend this variational formulation to a stochastic kinetic model. Our proposed inference method does not depend on any emulation of the ODE solution and only requires the extension of automatic differentiation to an ODE. We achieve this through a novel and holistic approach that uses both forward and adjoint sensitivity analysis techniques. Consequently, this approach can cater to both small and large ODE models efficiently. Upon benchmarking on some widely used mechanistic models, the proposed inference method produced a reliable approximation to the posterior distribution, with a significant reduction in execution time, in comparison to MCMC. } }
Endnote
%0 Conference Paper %T Variational inference for nonlinear ordinary differential equations %A Sanmitra Ghosh %A Paul Birrell %A Daniela De Angelis %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-ghosh21b %I PMLR %P 2719--2727 %U https://proceedings.mlr.press/v130/ghosh21b.html %V 130 %X We apply the reparameterisation trick to obtain a variational formulation of Bayesian inference in nonlinear ODE models. By invoking the linear noise approximation we also extend this variational formulation to a stochastic kinetic model. Our proposed inference method does not depend on any emulation of the ODE solution and only requires the extension of automatic differentiation to an ODE. We achieve this through a novel and holistic approach that uses both forward and adjoint sensitivity analysis techniques. Consequently, this approach can cater to both small and large ODE models efficiently. Upon benchmarking on some widely used mechanistic models, the proposed inference method produced a reliable approximation to the posterior distribution, with a significant reduction in execution time, in comparison to MCMC.
APA
Ghosh, S., Birrell, P. & De Angelis, D.. (2021). Variational inference for nonlinear ordinary differential equations . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:2719-2727 Available from https://proceedings.mlr.press/v130/ghosh21b.html.

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