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

TL;DR

This paper introduces a novel likelihood-free inference method for complex time-series models using signature kernels, enabling efficient and accurate posterior estimation even with limited data.

Contribution

It proposes a kernel classifier based on path signatures for sequential data, outperforming neural networks in low-sample scenarios for likelihood ratio estimation.

Findings

Signature kernel classifiers outperform neural networks with limited data.

The method provides efficient likelihood approximation for complex simulators.

Improved accuracy in posterior inference for time-series models.

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.