These notes expound the recent use of the signature transform and rough path
theory in data science and machine learning. We develop the core theory of the
signature from first principles and then survey some recent popular
applications of this approach, including signature-based kernel methods and
neural rough differential equations. The notes are based on a course given by
the two authors at Imperial College London.

这些笔记阐述了最近在数据科学和机器学习中使用签名变换和粗略路径理论。我们从第一原理发展了签名的核心理论，然后概述了一些最近流行的应用，包括基于签名的核方法和神经粗略微分方程。这些笔记是基于两位作者在伦敦帝国学院的课程。

粗路径讲义及其在机器学习中的应用

Lecture notes on rough paths and applications to machine learning

Signatory is a library for calculating and performing functionality related
to the signature and logsignature transforms. The focus is on machine learning,
and as such includes features such as CPU parallelism, GPU support, and
backpropagation. To our knowledge it is the first GPU-capable library for these
operations. Signatory implements new features not available in previous
libraries, such as efficient precomputation strategies. Furthermore, several
novel algorithmic improvements are introduced, producing substantial real-world
speedups even on the CPU without parallelism. The library operates as a Python
wrapper around C++, and is compatible with the PyTorch ecosystem. It may be
installed directly via \texttt{pip}. Source code, documentation, examples,
benchmarks and tests may be found at
\texttt{https://github.com/patrick-kidger/signatory}. The license is
Apache-2.0.

Signatory 是一个计算和执行与签名和日志签名变换相关功能的库，重点关注于机器学习，并包括 CPU 并行化，GPU 支持和反向传播等特性。