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

Dyer, Joel; Cannon, Patrick; Schmon, Sebastian M.; Camps-Valls, Gustau; Ruiz, Francisco J.R.; Valera, Isabel

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

Dyer, Joel; Cannon, Patrick; Schmon, Sebastian M.; Camps-Valls, Gustau; Ruiz, Francisco J.R.; Valera, Isabel

Authors

Joel Dyer

Patrick Cannon

Sebastian M. Schmon

Gustau Camps-Valls

Francisco J.R. Ruiz

Isabel Valera

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.

Citation

Dyer, J., Cannon, P., Schmon, S. M., Camps-Valls, G., Ruiz, F. J., & Valera, I. (2022). Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation.

Conference Name	Artificial Intelligence and Statistics 2022 (AISTATS): The 25th International Conference on Artificial Intelligence and Statistics
Conference Location	Virtual
Start Date	Mar 28, 2022
End Date	Mar 30, 2022
Acceptance Date	Jan 18, 2022
Online Publication Date	May 3, 2022
Publication Date	2022
Deposit Date	Jun 24, 2022
Publicly Available Date	Jun 24, 2022
Volume	151
Series Title	Proceedings of Machine Learning Research
Publisher URL	http://proceedings.mlr.press/v151/