Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation
This work addresses the challenge of statistical inference in complex simulation models without tractable likelihoods, offering a more efficient method for researchers in natural and social sciences, though it is incremental as it builds on existing likelihood ratio techniques.
The paper tackles the problem of likelihood-free inference for expensive time-series simulators by proposing a kernel classifier using path signatures, which outperforms sophisticated neural networks in low-sample scenarios for posterior inference tasks.
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.