# Signature Methods in Machine Learning

arXiv: https://arxiv.org/abs/2206.14674 · HTML: https://mlsanity.com/paper/2206.14674/

## 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 (most cited first, 30 of 38)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Publicly Available Clinical BERT Embeddings](https://mlsanity.com/paper/1904.03323/) (2019)
- [NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysis](https://mlsanity.com/paper/1604.02808/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [ClinicalBERT: Modeling Clinical Notes and Predicting Hospital Readmission](https://mlsanity.com/paper/1904.05342/) (2019)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [RMPE: Regional Multi-person Pose Estimation](https://mlsanity.com/paper/1612.00137/) (2016)
- [Transfer Learning in Biomedical Natural Language Processing: An Evaluation of BERT and ELMo on Ten Benchmarking Datasets](https://mlsanity.com/paper/1906.05474/) (2019)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Spatio-Temporal LSTM with Trust Gates for 3D Human Action Recognition](https://mlsanity.com/paper/1607.07043/) (2016)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [An End-to-End Spatio-Temporal Attention Model for Human Action Recognition from Skeleton Data](https://mlsanity.com/paper/1611.06067/) (2016)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Co-occurrence Feature Learning for Skeleton based Action Recognition using Regularized Deep LSTM Networks](https://mlsanity.com/paper/1603.07772/) (2016)
- [P-CNN: Pose-based CNN Features for Action Recognition](https://mlsanity.com/paper/1506.03607/) (2015)
- [The Signature Kernel is the solution of a Goursat PDE](https://mlsanity.com/paper/2006.14794/) (2020)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [Skeleton-Based Action Recognition Using Spatio-Temporal LSTM Network with Trust Gates](https://mlsanity.com/paper/1706.08276/) (2017)
- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Enhancing Clinical Concept Extraction with Contextual Embeddings](https://mlsanity.com/paper/1902.08691/) (2019)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Distribution Regression for Sequential Data](https://mlsanity.com/paper/2006.05805/) (2020)
- [Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition](https://mlsanity.com/paper/1707.03993/) (2017)

## Built on by (most cited first, 30 of 34)

- [Dynamical Survival Analysis with Controlled Latent States](https://mlsanity.com/paper/2401.17077/) (2024)
- [Sparse Signature Coefficient Recovery via Kernels](https://mlsanity.com/paper/2412.08579/) (2024)
- [The Volterra signature](https://mlsanity.com/paper/2603.04525/) (2026)
- [Novelty Detection on Radio Astronomy Data using Signatures](https://mlsanity.com/paper/2402.14892/) (2024)
- [Universal approximation with signatures of non-geometric rough paths](https://mlsanity.com/paper/2602.05898/) (2026)
- [Learning the Dynamics of Sparsely Observed Interacting Systems](https://mlsanity.com/paper/2301.11647/) (2023)
- [Sig-DEG for Distillation: Making Diffusion Models Faster and Lighter](https://mlsanity.com/paper/2508.16939/) (2025)
- [Global universal approximation with Brownian signatures](https://mlsanity.com/paper/2512.16396/) (2025)
- [Deep incremental learning models for financial temporal tabular datasets with distribution shifts](https://mlsanity.com/paper/2303.07925/) (2023)
- [Signature Isolation Forest](https://mlsanity.com/paper/2403.04405/) (2024)
- [Local regression on path spaces with signature metrics](https://mlsanity.com/paper/2510.16728/) (2025)
- [Path Signatures Enable Model-Free Mapping of RNA Modifications](https://mlsanity.com/paper/2511.08855/) (2025)
- [Generating Financial Time Series by Matching Random Convolutional Features](https://mlsanity.com/paper/2606.05138/) (2026)
- [Feature Engineering Methods on Multivariate Time-Series Data for Financial Data Science Competitions](https://mlsanity.com/paper/2303.16117/) (2023)
- [Generating drawdown-realistic financial price paths using path signatures](https://mlsanity.com/paper/2309.04507/) (2023)
- [Gaussian processes based data augmentation and expected signature for time series classification](https://mlsanity.com/paper/2310.10836/) (2023)
- [Path Signature Representation of Patient-Clinician Interactions as a Predictor for Neuropsychological Tests Outcomes in Children: A Proof of Concept](https://mlsanity.com/paper/2312.11512/) (2023)
- [Path Signatures and Graph Neural Networks for Slow Earthquake Analysis: Better Together?](https://mlsanity.com/paper/2402.03558/) (2024)
- [Fractional signature: a generalisation of the signature inspired by fractional calculus](https://mlsanity.com/paper/2407.17446/) (2024)
- [Scalable Signature Kernel Computations for Long Time Series via Local Neumann Series Expansions](https://mlsanity.com/paper/2502.20392/) (2025)
- [Power Spectrum Signatures of Graphs](https://mlsanity.com/paper/2503.09660/) (2025)
- [Detecting malignant dynamics on very few blood sample using signature coefficients](https://mlsanity.com/paper/2506.09097/) (2025)
- [Hypergraphs on high dimensional time series sets using signature transform](https://mlsanity.com/paper/2507.15802/) (2025)
- [Signature-Informed Transformer for Asset Allocation](https://mlsanity.com/paper/2510.03129/) (2025)
- [Novelty detection on path space](https://mlsanity.com/paper/2512.03243/) (2025)
- [Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecasting](https://mlsanity.com/paper/2602.10182/) (2026)
- [Global universality via discrete-time signatures](https://mlsanity.com/paper/2603.09773/) (2026)
- [Extending SSMs with the Exponentially Weighted Signature](https://mlsanity.com/paper/2603.19198/) (2026)
- [Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functions](https://mlsanity.com/paper/2604.04662/) (2026)
- [Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHS](https://mlsanity.com/paper/2604.05008/) (2026)

## 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.