Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation

Joel Dyer, Patrick W. Cannon, Sebastian M. Schmon
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:11131-11144, 2022.

Abstract

Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function, rendering traditional likelihood-based statistical inference impossible. Recent advances in machine learning have introduced novel algorithms for estimating otherwise intractable likelihood functions using a likelihood ratio trick based on binary classifiers. Consequently, efficient likelihood approximations can be obtained whenever good probabilistic classifiers can be constructed. We propose a kernel classifier for sequential data using path signatures based on the recently introduced signature kernel. We demonstrate that the representative power of signatures yields a highly performant classifier, even in the crucially important case where sample numbers are low. In such scenarios, our approach can outperform sophisticated neural networks for common posterior inference tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-dyer22a, title = { Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation }, author = {Dyer, Joel and Cannon, Patrick W. and Schmon, Sebastian M.}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {11131--11144}, 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/dyer22a/dyer22a.pdf}, url = {https://proceedings.mlr.press/v151/dyer22a.html}, abstract = { Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function, rendering traditional likelihood-based statistical inference impossible. Recent advances in machine learning have introduced novel algorithms for estimating otherwise intractable likelihood functions using a likelihood ratio trick based on binary classifiers. Consequently, efficient likelihood approximations can be obtained whenever good probabilistic classifiers can be constructed. We propose a kernel classifier for sequential data using path signatures based on the recently introduced signature kernel. We demonstrate that the representative power of signatures yields a highly performant classifier, even in the crucially important case where sample numbers are low. In such scenarios, our approach can outperform sophisticated neural networks for common posterior inference tasks. } }
Endnote
%0 Conference Paper %T Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation %A Joel Dyer %A Patrick W. Cannon %A Sebastian M. Schmon %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-dyer22a %I PMLR %P 11131--11144 %U https://proceedings.mlr.press/v151/dyer22a.html %V 151 %X Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function, rendering traditional likelihood-based statistical inference impossible. Recent advances in machine learning have introduced novel algorithms for estimating otherwise intractable likelihood functions using a likelihood ratio trick based on binary classifiers. Consequently, efficient likelihood approximations can be obtained whenever good probabilistic classifiers can be constructed. We propose a kernel classifier for sequential data using path signatures based on the recently introduced signature kernel. We demonstrate that the representative power of signatures yields a highly performant classifier, even in the crucially important case where sample numbers are low. In such scenarios, our approach can outperform sophisticated neural networks for common posterior inference tasks.
APA
Dyer, J., Cannon, P.W. & Schmon, S.M.. (2022). Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:11131-11144 Available from https://proceedings.mlr.press/v151/dyer22a.html.

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