Learning with Signatures

TL;DR

This paper explores the use of the Signature Transform in supervised learning, achieving high accuracy with minimal labels and fast CPU-based classification by leveraging harmonic analysis tools and optimal scale factors.

Contribution

It introduces a novel supervised framework utilizing signature and log-signature transforms, with a closed-form solution for optimal scale factors, enabling fast and accurate classification.

Findings

Achieved 100% accuracy on AFHQ, MNIST, and CIFAR10 datasets.

Classification is significantly faster at CPU level compared to other methods.

The framework requires minimal labels and no credit assignment.

Abstract

In this work we investigate the use of the Signature Transform in the context of Learning. Under this assumption, we advance a supervised framework that potentially provides state-of-the-art classification accuracy with the use of few labels without the need of credit assignment and with minimal or no overfitting. We leverage tools from harmonic analysis by the use of the signature and log-signature, and use as a score function RMSE and MAE Signature and log-signature. We develop a closed-form equation to compute probably good optimal scale factors, as well as the formulation to obtain them by optimization. Techniques of Signal Processing are addressed to further characterize the problem. Classification is performed at the CPU level orders of magnitude faster than other methods. We report results on AFHQ, MNIST and CIFAR10, achieving 100% accuracy on all tasks assuming we can determine at test time which probably good optimal scale factor to use for each category.