Functional linear regression with truncated signatures

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