mlsanityData to 7 Oct 2026

Signature moments to characterize laws of stochastic processes

arXiv 1810.10971 ↗First posted 25 Oct 2018math.ST math.PR stat.MLcited by 54

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Abstract (arXiv)

The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us to derive a metric of maximum mean discrepancy type for laws of stochastic processes and study the topology it induces on the space of laws of stochastic processes. This metric can be kernelized using the signature kernel which allows to efficiently compute it. As an application, we provide a non-parametric two-sample hypothesis test for laws of stochastic processes.

Key facts. Cited by 54 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Oct 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 4; 2023: 11; 2024: 9; 2025: 11; 2026: 12.

54 papers.

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  1. 2021Sig-Wasserstein GANs for Time Series Generationcited by 60
  2. 2022Signature Methods in Machine Learningcited by 33
  3. 2021Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processescited by 27
  4. 2023Global universal approximation of functional input maps on weighted spacescited by 19
  5. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  6. 2023PCF-GAN: generating sequential data via the characteristic function of measures on the path spacecited by 13
  7. 2021Signatured Deep Fictitious Play for Mean Field Games with Common Noisecited by 12
  8. 2021Approximate Bayesian Computation with Path Signaturescited by 12
  9. 2022Capturing Graphs with Hypo-Elliptic Diffusionscited by 12
  10. 2023New directions in the applications of rough path theorycited by 12
  11. 2023Random Fourier Signature Featurescited by 9
  12. 2024Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signalscited by 9
38 more
  1. 2023The Signature Kernelcited by 8
  2. 2024Time-Causal VAE: Robust Financial Time Series Generatorcited by 8
  3. 2021Feature Engineering with Regularity Structurescited by 7
  4. 2021Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysiscited by 6
  5. 2023Kernelized Cumulants: Beyond Kernel Mean Embeddingscited by 5
  6. 2021Deep Signature FBSDE Algorithmcited by 4
  7. 2023G-Signatures: Global Graph Propagation With Randomized Signaturescited by 4
  8. 2024Novelty Detection on Radio Astronomy Data using Signaturescited by 4
  9. 2022A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spacescited by 3
  10. 2024High Rank Path Development: an approach of learning the filtration of stochastic processescited by 3
  11. 2024Tensor learning with orthogonal, Lorentz, and symplectic symmetriescited by 3
  12. 2025Numerical Schemes for Signature Kernelscited by 3
  13. 2025Signature Maximum Mean Discrepancy Two-Sample Statistical Testscited by 3
  14. 2023Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structurescited by 2
  15. 2024Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEscited by 2
  16. 2026OpenFinGym: A Verifiable Multi-Task Gym Environment for Evaluating Quant Agentscited by 2
  17. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  18. 2024Transportation Marketplace Rate Forecast Using Signature Transformcited by 1
  19. 2024Signature Isolation Forestcited by 1
  20. 2025Expected Signature Kernels for L'evy Rough Pathscited by 1
  21. 2025Local regression on path spaces with signature metricscited by 1
  22. 2025Path Signatures Enable Model-Free Mapping of RNA Modificationscited by 1
  23. 2025Global universal approximation with Brownian signaturescited by 1
  24. 2026Generating Financial Time Series by Matching Random Convolutional Featurescited by 1
  25. 2022Learning the conditional law: signatures and conditional GANs in filtering and prediction of diffusion processescited by 0
  26. 2023Directed Chain Generative Adversarial Networkscited by 0
  27. 2023Generating drawdown-realistic financial price paths using path signaturescited by 0
  28. 2023Gaussian processes based data augmentation and expected signature for time series classificationcited by 0
  29. 2025Scalable Signature Kernel Computations for Long Time Series via Local Neumann Series Expansionscited by 0
  30. 2025SPDEBench: An Extensive Benchmark for Learning Stochastic PDEscited by 0
  31. 2025Tensor-to-Tensor Models with Fast Iterated Sum Featurescited by 0
  32. 2025Novelty detection on path spacecited by 0
  33. 2025SigMA: Path Signatures and Multi-head Attention for Learning Parameters in fBm-driven SDEscited by 0
  34. 2026Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecastingcited by 0
  35. 2026Global universality via discrete-time signaturescited by 0
  36. 2026Safety Certification is Classificationcited by 0
  37. 2026Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signalscited by 0
  38. 2026Learning Manifold and Ito Dynamics with Branched Neural Rough Differential Equationscited by 0

50 most cited of 54 All 54 (JSON)