论文标题
签名方法简介
Introduction to the signature method
论文作者
论文摘要
在地球科学中观察到的顺序数据可以被视为多维空间中的路径。为了有效地读取路径，将其转换为一个称为签名的数字序列很有用，该数字可以忠实地描述路径中的点和非线性的顺序。特别是，可以使用签名中的术语的线性组合来近似在一组路径上定义的任何非线性函数。因此，当人们学习一组带有标签的顺序数据时，可以将线性回归应用于签名和标签对，即使标签是由非线性函数确定的，它们也将获得高性能学习。通过使用顺序数据将签名方法纳入机器学习和数据同化，可以预期我们可以提取以前被忽略的信息。
The sequential data observed in earth science can be regarded as paths in multidimensional space. To read the path effectively, it is useful to convert it into a sequence of numbers called the signature, which can faithfully describe the order of points and nonlinearity in the path. In particular, a linear combination of the terms in a signature can be used to approximate any nonlinear function defined on a set of paths. Thereby, when one learns a set of sequential data with labels attached to it, linear regression can be applied to the pairs of signature and label, which will achieve high performance learning even when the labels are determined by a nonlinear function. By incorporating the signature methods into machine learning and data assimilation utilizing sequential data, it is expected that we can extract information that has previously been overlooked.
