Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:44454455, 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 mixedeffects (NLME) dynamical systems, the statistical workhorse for many experimental sciences. We cast parameter inference as stochastic optimisation of an endtoend differentiable, blockconditional variational autoencoder. We specify the dynamics of the datagenerating 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 righthand sides can be a mixture of userprescribed or "whitebox" subcomponents and neural network or "blackbox" subcomponents. 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 “zeroshot" learning). We empirically validate our method by predicting the dynamic behaviour of bacteria that were genetically engineered to function as biosensors.
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