The iisignature library: efficient calculation of iterated-integral signatures and log signatures

TL;DR

This paper introduces efficient algorithms for calculating iterated-integral signatures and log signatures of paths, which are useful in rough path theory, statistics, and machine learning, and provides a Python package implementation.

Contribution

The paper presents novel algorithms for fast computation of signatures and log signatures, and releases a Python package for practical use.

Findings

Algorithms outperform existing methods in speed

The Python package facilitates easy integration into workflows

Benchmark results demonstrate efficiency gains

Abstract

Iterated-integral signatures and log signatures are vectors calculated from a path that characterise its shape. They come from the theory of differential equations driven by rough paths, and also have applications in statistics and machine learning. We present algorithms for efficiently calculating these signatures, and benchmark their performance. We release the methods as a Python package.