Differentiable Likelihoods for Fast Inversion of ’Likelihood-Free’ Dynamical Systems

Hans Kersting, Nicholas Krämer, Martin Schiegg, Christian Daniel, Michael Tiemann, Philipp Hennig
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5198-5208, 2020.

Abstract

Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-kersting20a, title = {Differentiable Likelihoods for Fast Inversion of ’{L}ikelihood-Free’ Dynamical Systems}, author = {Kersting, Hans and Kr{\"a}mer, Nicholas and Schiegg, Martin and Daniel, Christian and Tiemann, Michael and Hennig, Philipp}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5198--5208}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/kersting20a/kersting20a.pdf}, url = {https://proceedings.mlr.press/v119/kersting20a.html}, abstract = {Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems.} }
Endnote
%0 Conference Paper %T Differentiable Likelihoods for Fast Inversion of ’Likelihood-Free’ Dynamical Systems %A Hans Kersting %A Nicholas Krämer %A Martin Schiegg %A Christian Daniel %A Michael Tiemann %A Philipp Hennig %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-kersting20a %I PMLR %P 5198--5208 %U https://proceedings.mlr.press/v119/kersting20a.html %V 119 %X Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems.
APA
Kersting, H., Krämer, N., Schiegg, M., Daniel, C., Tiemann, M. & Hennig, P.. (2020). Differentiable Likelihoods for Fast Inversion of ’Likelihood-Free’ Dynamical Systems. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5198-5208 Available from https://proceedings.mlr.press/v119/kersting20a.html.

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