mlsanityData to 14 Oct 2026

Kernels for sequentially ordered data

arXiv 1601.08169 ↗First posted 29 Jan 2016stat.ML cs.DM cs.LGcited by 84

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Abstract (arXiv)

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a "sequentialized" version of any static kernel. The sequential kernels are efficiently computable for discrete sequences and are shown to approximate a continuous moment form in a sampling sense. A number of known kernels for sequences arise as "sequentializations" of suitable static kernels: string kernels may be obtained as a special case, and alignment kernels are closely related up to a modification that resolves their open non-definiteness issue. Our experiments indicate that our signature-based sequential kernel framework may be a promising approach to learning with sequential data, such as time series, that allows to avoid extensive manual pre-processing.

Key facts. Cited by 84 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 Jan 2016.

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Citing papers per year: 2021: 12; 2022: 12; 2023: 16; 2024: 10; 2025: 17; 2026: 17.

84 papers.

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  1. 2021Neural SDEs as Infinite-Dimensional GANscited by 161
  2. 2021Efficient and Accurate Gradients for Neural SDEscited by 71
  3. 2022Signature Methods in Machine Learningcited by 34
  4. 2021Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processescited by 27
  5. 2023Neural signature kernels as infinite-width-depth-limits of controlled ResNetscited by 25
  6. 2021Framing RNN as a kernel method: A neural ODE approachcited by 23
  7. 2021SigGPDE: Scaling Sparse Gaussian Processes on Sequential Datacited by 22
  8. 2023Koopman Kernel Regressioncited by 22
  9. 2023Global universal approximation of functional input maps on weighted spacescited by 19
  10. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  11. 2025Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Modelscited by 18
  12. 2021Signatured Deep Fictitious Play for Mean Field Games with Common Noisecited by 12
38 more
  1. 2021Approximate Bayesian Computation with Path Signaturescited by 12
  2. 2022Capturing Graphs with Hypo-Elliptic Diffusionscited by 12
  3. 2023New directions in the applications of rough path theorycited by 12
  4. 2021Logsig-RNN: a novel network for robust and efficient skeleton-based action recognitioncited by 11
  5. 2022Chaotic Hedging with Iterated Integrals and Neural Networkscited by 10
  6. 2022Applications of Signature Methods to Market Anomaly Detectioncited by 9
  7. 2022A kernel Stein test of goodness of fit for sequential modelscited by 9
  8. 2023Random Fourier Signature Featurescited by 9
  9. 2024Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signalscited by 9
  10. 2022Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimationcited by 8
  11. 2022Reservoir kernels and Volterra seriescited by 8
  12. 2023The Signature Kernelcited by 8
  13. 2023A Bias-Variance-Covariance Decomposition of Kernel Scores for Generative Modelscited by 8
  14. 2021Feature Engineering with Regularity Structurescited by 7
  15. 2022Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEscited by 7
  16. 2023Infinite-dimensional reservoir computingcited by 7
  17. 2023SigFormer: Signature Transformers for Deep Hedgingcited by 7
  18. 2025In-Context Learning of Stochastic Differential Equations with Foundation Inference Modelscited by 7
  19. 2022Maximum Mean Discrepancy on Exponential Windows for Online Change Detectioncited by 6
  20. 2025Koopman-Equivariant Gaussian Processescited by 6
  21. 2025pySigLib -- Fast Signature-Based Computations on CPU and GPUcited by 6
  22. 2023Kernelized Cumulants: Beyond Kernel Mean Embeddingscited by 5
  23. 2023Nystr"om M-Hilbert-Schmidt Independence Criterioncited by 5
  24. 2026The Volterra signaturecited by 5
  25. 2021Deep Signature FBSDE Algorithmcited by 4
  26. 2023Path Signatures for Diversity in Probabilistic Trajectory Optimisationcited by 3
  27. 2025Numerical Schemes for Signature Kernelscited by 3
  28. 2025Signature Maximum Mean Discrepancy Two-Sample Statistical Testscited by 3
  29. 2021Keep it Tighter -- A Story on Analytical Mean Embeddingscited by 2
  30. 20222-d signature of images and texture classificationcited by 2
  31. 2024Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEscited by 2
  32. 2025Signature Kernel Scoring Rule: A Spatio-Temporal Diagnostic for Probabilistic Weather Forecastingcited by 2
  33. 2025Global universal approximation with Brownian signaturescited by 2
  34. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  35. 2021Path classification by stochastic linear recurrent neural networkscited by 1
  36. 2023FRUITS: Feature Extraction Using Iterated Sums for Time Series Classificationcited by 1
  37. 2024Transportation Marketplace Rate Forecast Using Signature Transformcited by 1
  38. 2024Signature Isolation Forestcited by 1

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