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.

翻译：我们将自己置于功能回归环境之中,并提出了一种在矢量价值的功能共变中回归实际产出的新方法。这种方法基于签名的概念,它表示一个函数是其迭代整体的无限系列。签名关键取决于一个短径参数,为该参数提供估算器,同时提供理论保证。关于模拟和真实世界数据集的经验研究表明,由此产生的方法与传统的功能线性模型具有竞争力,特别是当功能共变在高维空间中取其值时。