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

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, March). Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation. Presented at Artificial Intelligence and Statistics 2022 (AISTATS): The 25th International Conference on Artificial Intelligence and Statistics, Virtual

• Presentation Conference Type: Conference Paper (published)
• Conference Name: Artificial Intelligence and Statistics 2022 (AISTATS): The 25th International Conference on Artificial Intelligence and Statistics
• 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
• Public URL: https://durham-repository.worktribe.com/output/1136622
• Publisher URL: http://proceedings.mlr.press/v151/