mlsanityData to 7 Oct 2026

The Signature Kernel

arXiv 2305.04625 ↗First posted 8 May 2023math.PR cs.LG stat.MLcited by 8

Not on the map. Why?

Abstract (arXiv)

The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and shows strong empirical performance. In this short survey paper for a forthcoming Springer handbook, we give an elementary introduction to the signature kernel and highlight these theoretical and computational properties.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 20 of its 77 references that are in the map. First posted on arXiv 8 May 2023.

Builds on

20 of 77 references.

References · 20

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
  3. 2016A Primer on the Signature Method in Machine Learningcited by 100
  4. 2016Kernels for sequentially ordered datacited by 83
  5. 2020The Signature Kernel is the solution of a Goursat PDEcited by 58
  6. 2018Signature moments to characterize laws of stochastic processescited by 54
  7. 2020Metrizing Weak Convergence with Maximum Mean Discrepanciescited by 35
  8. 2020A Data-driven Market Simulator for Small Data Environmentscited by 34
  9. 2021Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processescited by 27
  10. 2023Neural signature kernels as infinite-width-depth-limits of controlled ResNetscited by 25
  11. 2021Framing RNN as a kernel method: A neural ODE approachcited by 23
  12. 2021SigGPDE: Scaling Sparse Gaussian Processes on Sequential Datacited by 22
8 more
  1. 2018Persistence paths and signature features in topological data analysiscited by 17
  2. 2022Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimationcited by 8
  3. 2020Functional linear regression with truncated signaturescited by 6
  4. 2020Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projectionscited by 5
  5. 2020Path Signatures on Lie Groupscited by 4
  6. 2021Nonlinear Independent Component Analysis for Discrete-Time and Continuous-Time Signalscited by 4
  7. 2020Generalized iterated-sums signaturescited by 3
  8. 2023A Robustness Analysis of Blind Source Separationcited by 2

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 3; 2025: 4.

8 papers.

  1. 2023Koopman Kernel Regressioncited by 22
  2. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  3. 2025Koopman-Equivariant Gaussian Processescited by 6
  4. 2025Kernel-based estimators for functional causal effectscited by 3
  5. 2024Signature Isolation Forestcited by 1
  6. 2024Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detectioncited by 1
  7. 2025Local regression on path spaces with signature metricscited by 1
  8. 2025Scalable Signature Kernel Computations for Long Time Series via Local Neumann Series Expansionscited by 0