论文标题
具有截短签名的功能线性回归
Functional linear regression with truncated signatures
论文作者
论文摘要
我们将自己置于功能回归环境中，并提出了一种新的方法，用于回归矢量值功能协变量的实际输出。该方法基于签名的概念，签名的概念是将功能作为无限序列的迭代积分的表示。该签名至关重要地取决于提供估计器的截断参数以及理论保证。对模拟和现实世界数据集的一项实证研究表明，所得的方法与传统的功能线性模型具有竞争力，特别是当功能协变量将其值置于高维空间时。
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.
