mlsanityData to 14 Oct 2026

Signature Methods in Machine Learning

arXiv 2206.14674 ↗First posted 29 Jun 2022stat.ML cs.LG cs.NAcited by 34

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Abstract (arXiv)

Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps because of their mathematical precision, have proved useful in analysing streamed data in situations where the data is irregular, and not stationary, and the dimension of the data and the sample sizes are both moderate. Understanding streamed multi-modal data is exponential: a word in n letters from an alphabet of size d can be any one of dn messages. Signatures remove the exponential amount of noise that arises from sampling irregularity, but an exponential amount of information still remain. This survey aims to stay in the domain where that exponential scaling can be managed directly. Scalability issues are an important challenge in many problems but would require another survey article and further ideas. This survey describes a range of contexts where the data sets are small enough to remove the possibility of massive machine learning, and the existence of small sets of context free and principled features can be used effectively. The mathematical nature of the tools can make their use intimidating to non-mathematicians. The examples presented in this article are intended to bridge this communication gap and provide tractable working examples drawn from the machine learning context. Notebooks are available online for several of these examples. This survey builds on the earlier paper of Ilya Chevryev and Andrey Kormilitzin which had broadly similar aims at an earlier point in the development of this machinery. This article illustrates how the theoretical insights offered by signatures are simply realised in the analysis of application data in a way that is largely agnostic to the data type.

Key facts. Cited by 34 papers in the map (data through 14 Oct 2026). Builds on 38 of its 170 references that are in the map. First posted on arXiv 29 Jun 2022.

Builds on

38 of 170 references.

References · 38

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2018Deep contextualized word representationscited by 2,290
  4. 2019Publicly Available Clinical BERT Embeddingscited by 1,002
  5. 2016NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysiscited by 686
  6. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
  7. 2019ClinicalBERT: Modeling Clinical Notes and Predicting Hospital Readmissioncited by 493
  8. 2019Deep Learning for Anomaly Detection: A Surveycited by 358
  9. 2016RMPE: Regional Multi-person Pose Estimationcited by 340
  10. 2019Transfer Learning in Biomedical Natural Language Processing: An Evaluation of BERT and ELMo on Ten Benchmarking Datasetscited by 299
  11. 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 183
  12. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 176
26 more
  1. 2021Neural SDEs as Infinite-Dimensional GANscited by 161
  2. 2016Spatio-Temporal LSTM with Trust Gates for 3D Human Action Recognitioncited by 143
  3. 2020Neural Rough Differential Equations for Long Time Seriescited by 143
  4. 2016An End-to-End Spatio-Temporal Attention Model for Human Action Recognition from Skeleton Datacited by 126
  5. 2016A Primer on the Signature Method in Machine Learningcited by 104
  6. 2016Kernels for sequentially ordered datacited by 84
  7. 2016Co-occurrence Feature Learning for Skeleton based Action Recognition using Regularized Deep LSTM Networkscited by 63
  8. 2015P-CNN: Pose-based CNN Features for Action Recognitioncited by 58
  9. 2020The Signature Kernel is the solution of a Goursat PDEcited by 58
  10. 2018Signature moments to characterize laws of stochastic processescited by 56
  11. 2017Skeleton-Based Action Recognition Using Spatio-Temporal LSTM Network with Trust Gatescited by 54
  12. 2014Learning Theory for Distribution Regressioncited by 48
  13. 2019Enhancing Clinical Concept Extraction with Contextual Embeddingscited by 48
  14. 2020Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPUcited by 46
  15. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  16. 2018The iisignature library: efficient calculation of iterated-integral signatures and log signaturescited by 40
  17. 2020Distribution Regression for Sequential Datacited by 31
  18. 2017Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognitioncited by 20
  19. 2017Attentive Convolutional Neural Network based Speech Emotion Recognition: A Study on the Impact of Input Features, Signal Length, and Acted Speechcited by 18
  20. 2017A signature-based machine learning model for bipolar disorder and borderline personality disordercited by 15
  21. 2017Bayesian Approaches to Distribution Regressioncited by 9
  22. 2020Dimensionless Anomaly Detection on Multivariate Streams with Variance Norm and Path Signaturecited by 8
  23. 2018NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equationscited by 7
  24. 2020Learning to Detect Bipolar Disorder and Borderline Personality Disorder with Language and Speech in Non-Clinical Interviewscited by 5
  25. 2017Advanced LSTM: A Study about Better Time Dependency Modeling in Emotion Recognitioncited by 3
  26. 2020Information Extraction from Swedish Medical Prescriptions with Sig-Transformer Encodercited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 6; 2025: 10; 2026: 12.

34 papers.

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  1. 2024Dynamical Survival Analysis with Controlled Latent Statescited by 7
  2. 2024Sparse Signature Coefficient Recovery via Kernelscited by 6
  3. 2026The Volterra signaturecited by 5
  4. 2024Novelty Detection on Radio Astronomy Data using Signaturescited by 4
  5. 2026Universal approximation with signatures of non-geometric rough pathscited by 4
  6. 2023Learning the Dynamics of Sparsely Observed Interacting Systemscited by 3
  7. 2025Sig-DEG for Distillation: Making Diffusion Models Faster and Lightercited by 3
  8. 2025Global universal approximation with Brownian signaturescited by 2
  9. 2023Deep incremental learning models for financial temporal tabular datasets with distribution shiftscited by 1
  10. 2024Signature Isolation Forestcited by 1
  11. 2025Local regression on path spaces with signature metricscited by 1
  12. 2025Path Signatures Enable Model-Free Mapping of RNA Modificationscited by 1
22 more
  1. 2026Generating Financial Time Series by Matching Random Convolutional Featurescited by 1
  2. 2023Feature Engineering Methods on Multivariate Time-Series Data for Financial Data Science Competitionscited by 0
  3. 2023Generating drawdown-realistic financial price paths using path signaturescited by 0
  4. 2023Gaussian processes based data augmentation and expected signature for time series classificationcited by 0
  5. 2023Path Signature Representation of Patient-Clinician Interactions as a Predictor for Neuropsychological Tests Outcomes in Children: A Proof of Conceptcited by 0
  6. 2024Path Signatures and Graph Neural Networks for Slow Earthquake Analysis: Better Together?cited by 0
  7. 2024Fractional signature: a generalisation of the signature inspired by fractional calculuscited by 0
  8. 2025Scalable Signature Kernel Computations for Long Time Series via Local Neumann Series Expansionscited by 0
  9. 2025Power Spectrum Signatures of Graphscited by 0
  10. 2025Detecting malignant dynamics on very few blood sample using signature coefficientscited by 0
  11. 2025Hypergraphs on high dimensional time series sets using signature transformcited by 0
  12. 2025Signature-Informed Transformer for Asset Allocationcited by 0
  13. 2025Novelty detection on path spacecited by 0
  14. 2026Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecastingcited by 0
  15. 2026Global universality via discrete-time signaturescited by 0
  16. 2026Extending SSMs with the Exponentially Weighted Signaturecited by 0
  17. 2026Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functionscited by 0
  18. 2026Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHScited by 0
  19. 2026Branched Signature Kernel Solvers for ODEs with rough Single-Trajectory signalscited by 0
  20. 2026Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEscited by 0
  21. 2026Tradable Ito Signatures: A Model-Free, Interpretable Framework for Dynamic Hedgingcited by 0
  22. 2026A Heisenberg Lift Descriptor for Order Sensitive Online Handwriting Recognitioncited by 0