Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems

Geoffrey Roeder, Paul Grant, Andrew Phillips, Neil Dalchau, Edward Meeds
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4445-4455, 2019.

Abstract

We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse for many experimental sciences. We cast parameter inference as stochastic optimisation of an end-to-end differentiable, block-conditional variational autoencoder. We specify the dynamics of the data-generating process as an ordinary differential equation (ODE) such that both the ODE and its solver are fully differentiable. This model class is highly flexible: the ODE right-hand sides can be a mixture of user-prescribed or "white-box" sub-components and neural network or "black-box" sub-components. Using stochastic optimisation, our amortised inference algorithm could seamlessly scale up to massive data collection pipelines (common in labs with robotic automation). Finally, our framework supports interpretability with respect to the underlying dynamics, as well as predictive generalization to unseen combinations of group components (also called “zero-shot" learning). We empirically validate our method by predicting the dynamic behaviour of bacteria that were genetically engineered to function as biosensors.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-meeds19a, title = {Efficient Amortised {B}ayesian Inference for Hierarchical and Nonlinear Dynamical Systems}, author = {Roeder, Geoffrey, and Grant, Paul and Phillips, Andrew and Dalchau, Neil, and Meeds, Edward}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {4445--4455}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/meeds19a/meeds19a.pdf}, url = {https://proceedings.mlr.press/v97/meeds19a.html}, abstract = {We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse for many experimental sciences. We cast parameter inference as stochastic optimisation of an end-to-end differentiable, block-conditional variational autoencoder. We specify the dynamics of the data-generating process as an ordinary differential equation (ODE) such that both the ODE and its solver are fully differentiable. This model class is highly flexible: the ODE right-hand sides can be a mixture of user-prescribed or "white-box" sub-components and neural network or "black-box" sub-components. Using stochastic optimisation, our amortised inference algorithm could seamlessly scale up to massive data collection pipelines (common in labs with robotic automation). Finally, our framework supports interpretability with respect to the underlying dynamics, as well as predictive generalization to unseen combinations of group components (also called “zero-shot" learning). We empirically validate our method by predicting the dynamic behaviour of bacteria that were genetically engineered to function as biosensors.} }
Endnote
%0 Conference Paper %T Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems %A Geoffrey Roeder %A Paul Grant %A Andrew Phillips %A Neil Dalchau %A Edward Meeds %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-meeds19a %I PMLR %P 4445--4455 %U https://proceedings.mlr.press/v97/meeds19a.html %V 97 %X We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse for many experimental sciences. We cast parameter inference as stochastic optimisation of an end-to-end differentiable, block-conditional variational autoencoder. We specify the dynamics of the data-generating process as an ordinary differential equation (ODE) such that both the ODE and its solver are fully differentiable. This model class is highly flexible: the ODE right-hand sides can be a mixture of user-prescribed or "white-box" sub-components and neural network or "black-box" sub-components. Using stochastic optimisation, our amortised inference algorithm could seamlessly scale up to massive data collection pipelines (common in labs with robotic automation). Finally, our framework supports interpretability with respect to the underlying dynamics, as well as predictive generalization to unseen combinations of group components (also called “zero-shot" learning). We empirically validate our method by predicting the dynamic behaviour of bacteria that were genetically engineered to function as biosensors.
APA
Roeder, G., Grant, P., Phillips, A., Dalchau, N. & Meeds, E.. (2019). Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:4445-4455 Available from https://proceedings.mlr.press/v97/meeds19a.html.

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