# Approximate Bayesian Computation with Path Signatures

arXiv: https://arxiv.org/abs/2106.12555 · HTML: https://mlsanity.com/paper/2106.12555/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 78 references that are in the map.
- First posted on arXiv 23 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Generalized Variational Inference: Three arguments for deriving new Posteriors](https://mlsanity.com/paper/1904.02063/) (2019)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [Statistical Inference for Generative Models with Maximum Mean Discrepancy](https://mlsanity.com/paper/1906.05944/) (2019)
- [Approximate Bayesian computation with the Wasserstein distance](https://mlsanity.com/paper/1905.03747/) (2019)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Learning Spatial-Semantic Context with Fully Convolutional Recurrent Network for Online Handwritten Chinese Text Recognition](https://mlsanity.com/paper/1610.02616/) (2016)
- [Generalized Posteriors in Approximate Bayesian Computation](https://mlsanity.com/paper/2011.08644/) (2020)
- [A Transportation Lp Distance for Signal Analysis](https://mlsanity.com/paper/1609.08669/) (2016)
- [A Comparison of Likelihood-Free Methods With and Without Summary Statistics](https://mlsanity.com/paper/2103.02407/) (2021)
- [Random graph models for dynamic networks](https://mlsanity.com/paper/1607.07570/) (2016)
- [Approximate Bayesian computation via the energy statistic](https://mlsanity.com/paper/1905.05884/) (2019)
- [A Generalised Signature Method for Multivariate Time Series Feature Extraction](https://mlsanity.com/paper/2006.00873/) (2020)
- [Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptotics](https://mlsanity.com/paper/2104.06384/) (2021)
- [Summary Statistics in Approximate Bayesian Computation](https://mlsanity.com/paper/1512.05633/) (2015)
- [Bayesian Learning from Sequential Data using Gaussian Processes with Signature Covariances](https://mlsanity.com/paper/1906.08215/) (2019)

## Built on by (most cited first, 12 of 12)

- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [On learning agent-based models from data](https://mlsanity.com/paper/2205.05052/) (2022)
- [Black-box Bayesian inference for economic agent-based models](https://mlsanity.com/paper/2202.00625/) (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)
- [Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation](https://mlsanity.com/paper/2202.11585/) (2022)
- [Calibrating Agent-based Models to Microdata with Graph Neural Networks](https://mlsanity.com/paper/2206.07570/) (2022)
- [Expected Signature Kernels for Rough Paths](https://mlsanity.com/paper/2509.07893/) (2025)
- [Directed Chain Generative Adversarial Networks](https://mlsanity.com/paper/2304.13131/) (2023)
- [Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputs](https://mlsanity.com/paper/2506.15845/) (2025)

## Abstract (arXiv)

Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data through some distance measure, but existing approaches are often poorly suited to time series simulators, for example due to an independent and identically distributed data assumption. In this paper, we propose to use path signatures in approximate Bayesian computation to handle the sequential nature of time series. We provide theoretical guarantees on the resultant posteriors and demonstrate competitive Bayesian parameter inference for simulators generating univariate, multivariate, irregularly spaced, and even non-Euclidean sequences.