# The Signature Kernel

arXiv: https://arxiv.org/abs/2305.04625 · HTML: https://mlsanity.com/paper/2305.04625/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 77 references that are in the map.
- First posted on arXiv 8 May 2023.

## Builds on (most cited first, 20 of 20)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [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)
- [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)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [A Data-driven Market Simulator for Small Data Environments](https://mlsanity.com/paper/2006.14498/) (2020)
- [Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes](https://mlsanity.com/paper/2109.03582/) (2021)
- [Neural signature kernels as infinite-width-depth-limits of controlled ResNets](https://mlsanity.com/paper/2303.17671/) (2023)
- [Framing RNN as a kernel method: A neural ODE approach](https://mlsanity.com/paper/2106.01202/) (2021)
- [SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data](https://mlsanity.com/paper/2105.04211/) (2021)
- [Persistence paths and signature features in topological data analysis](https://mlsanity.com/paper/1806.00381/) (2018)
- [Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation](https://mlsanity.com/paper/2202.11585/) (2022)
- [Functional linear regression with truncated signatures](https://mlsanity.com/paper/2006.08442/) (2020)
- [Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projections](https://mlsanity.com/paper/2006.07027/) (2020)
- [Path Signatures on Lie Groups](https://mlsanity.com/paper/2007.06633/) (2020)
- [Nonlinear Independent Component Analysis for Discrete-Time and Continuous-Time Signals](https://mlsanity.com/paper/2102.02876/) (2021)
- [Generalized iterated-sums signatures](https://mlsanity.com/paper/2012.04597/) (2020)
- [A Robustness Analysis of Blind Source Separation](https://mlsanity.com/paper/2303.10104/) (2023)

## Built on by (most cited first, 8 of 8)

- [Koopman Kernel Regression](https://mlsanity.com/paper/2305.16215/) (2023)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Kernel-based estimators for functional causal effects](https://mlsanity.com/paper/2503.05024/) (2025)
- [Signature Isolation Forest](https://mlsanity.com/paper/2403.04405/) (2024)
- [Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detection](https://mlsanity.com/paper/2407.11873/) (2024)
- [Local regression on path spaces with signature metrics](https://mlsanity.com/paper/2510.16728/) (2025)
- [Scalable Signature Kernel Computations for Long Time Series via Local Neumann Series Expansions](https://mlsanity.com/paper/2502.20392/) (2025)

## 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.