  We place ourselves in a functional regression setting and propose a novel
methodology for regressing a real output on vector-valued functional
covariates. This methodology is based on the notion of signature, which is a
representation of a function as an infinite series of its iterated integrals.
The signature depends crucially on a truncation parameter for which an
estimator is provided, together with theoretical guarantees. An empirical study
on both simulated and real-world datasets shows that the resulting methodology
is competitive with traditional functional linear models, in particular when
the functional covariates take their values in a high dimensional space.

Methodology