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

arXiv: https://arxiv.org/abs/2202.11585 · HTML: https://mlsanity.com/paper/2202.11585/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 51 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network](https://mlsanity.com/paper/1510.02175/) (2015)
- [Approximate Bayesian computation with the Wasserstein distance](https://mlsanity.com/paper/1905.03747/) (2019)
- [Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Setting](https://mlsanity.com/paper/2002.10399/) (2020)
- [Black-box Bayesian inference for economic agent-based models](https://mlsanity.com/paper/2202.00625/) (2022)
- [Approximate Bayesian Computation with Path Signatures](https://mlsanity.com/paper/2106.12555/) (2021)
- [Dynamic Likelihood-free Inference via Ratio Estimation (DIRE)](https://mlsanity.com/paper/1810.09899/) (2018)
- [Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptotics](https://mlsanity.com/paper/2104.06384/) (2021)

## Built on by (most cited first, 8 of 8)

- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [Random Fourier Signature Features](https://mlsanity.com/paper/2311.12214/) (2023)
- [Compositional simulation-based inference for time series](https://mlsanity.com/paper/2411.02728/) (2024)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [The Signature Kernel](https://mlsanity.com/paper/2305.04625/) (2023)
- [Calibrating Agent-based Models to Microdata with Graph Neural Networks](https://mlsanity.com/paper/2206.07570/) (2022)
- [Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings](https://mlsanity.com/paper/2403.07454/) (2024)

## Abstract (arXiv)

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.