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

• URL: http://arxiv.org/abs/2202.11585v1
• Date: Wed, 23 Feb 2022 15:59:34 GMT
• Title: Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation
• Authors: Joel Dyer, Patrick Cannon, Sebastian M Schmon
• Abstract summary: Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function. Recent advances in machine learning have introduced novel algorithms for estimating otherwise intractable likelihood functions. We propose a kernel classifier for sequential data using path signatures based on the recently introduced signature kernel.
• Score: 1.675857332621569
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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