Learning with Signatures

Abstract

Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. The present article is concerned with a novel approach for sequential learning, called the signature method and rooted in rough path theory. Its basic principle is to represent multidimensional paths, i.e., functions from [0, 1] to R𝑑, by a graded feature set of their iterated integrals, called the signature. This approach relies critically on an embedding principle, which consists in representing discretely sampled data as continuous paths. After a survey of basic principles of signatures, we investigate the influence of embeddings on prediction accuracy with an in-depth study of recent and challenging datasets. We show that a specific embedding, called lead-lag, is systematically better, whatever the dataset or algorithm used.