  Sequential and temporal data arise in many fields of research, such as
quantitative finance, medicine, or computer vision. A novel approach for
sequential learning, called the signature method and rooted in rough path
theory, is considered. Its basic principle is to represent multidimensional
paths 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 paths, i.e., functions from
$[0,1]$ to $\mathbb{R}^d$. After a survey of machine learning methodologies for
signatures, the influence of embeddings on prediction accuracy is investigated
with an in-depth study of three recent and challenging datasets. It is shown
that a specific embedding, called lead-lag, is systematically the strongest
performer across all datasets and algorithms considered. Moreover, an empirical
study reveals that computing signatures over the whole path domain does not
lead to a loss of local information. It is concluded that, with a good
embedding, combining signatures with other simple algorithms achieves results
competitive with state-of-the-art, domain-specific approaches.
