mlsanityData to 14 Oct 2026

Approximate Bayesian Computation with Path Signatures

arXiv 2106.12555 ↗First posted 23 Jun 2021stat.ME stat.CO stat.MLcited by 12

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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.

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

20 of 78 references.

References · 20

  1. 2013A General Framework for Updating Belief Distributionscited by 175
  2. 2016A Primer on the Signature Method in Machine Learningcited by 104
  3. 2016Kernels for sequentially ordered datacited by 84
  4. 2019Deep Signature Transformscited by 75
  5. 2020The Signature Kernel is the solution of a Goursat PDEcited by 58
  6. 2019Generalized Variational Inference: Three arguments for deriving new Posteriorscited by 57
  7. 2018Signature moments to characterize laws of stochastic processescited by 56
  8. 2019Statistical Inference for Generative Models with Maximum Mean Discrepancycited by 45
  9. 2019Approximate Bayesian computation with the Wasserstein distancecited by 34
  10. 2015Robust Bayesian inference via coarseningcited by 32
  11. 2016Learning Spatial-Semantic Context with Fully Convolutional Recurrent Network for Online Handwritten Chinese Text Recognitioncited by 19
  12. 2020Generalized Posteriors in Approximate Bayesian Computationcited by 19
8 more
  1. 2016A Transportation Lp Distance for Signal Analysiscited by 11
  2. 2021A Comparison of Likelihood-Free Methods With and Without Summary Statisticscited by 9
  3. 2016Random graph models for dynamic networkscited by 6
  4. 2019Approximate Bayesian computation via the energy statisticcited by 6
  5. 2020A Generalised Signature Method for Multivariate Time Series Feature Extractioncited by 5
  6. 2021Optimal scaling of random-walk Metropolis algorithms using Bayesian large-sample asymptoticscited by 4
  7. 2015Summary Statistics in Approximate Bayesian Computationcited by 3
  8. 2019Bayesian Learning from Sequential Data using Gaussian Processes with Signature Covariancescited by 3

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Cited by year

Citing papers per year: 2022: 6; 2023: 2; 2024: 2; 2025: 2.

12 papers.

  1. 2024All-in-one simulation-based inferencecited by 74
  2. 2022Robust Neural Posterior Estimation and Statistical Model Criticismcited by 46
  3. 2022Investigating the Impact of Model Misspecification in Neural Simulation-based Inferencecited by 45
  4. 2022On learning agent-based models from datacited by 14
  5. 2022Black-box Bayesian inference for economic agent-based modelscited by 13
  6. 2023Random Fourier Signature Featurescited by 9
  7. 2024Compositional simulation-based inference for time seriescited by 9
  8. 2022Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimationcited by 8
  9. 2022Calibrating Agent-based Models to Microdata with Graph Neural Networkscited by 7
  10. 2025Expected Signature Kernels for Rough Pathscited by 1
  11. 2023Directed Chain Generative Adversarial Networkscited by 0
  12. 2025Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputscited by 0