This article provides a concise overview of some of the recent advances in the application of rough path theory to machine learning. Controlled differential equations (CDEs) are discussed as the key mathematical model to describe the interaction of a stream with a physical control system. A collection of iterated integrals known as the signature naturally arises in the description of the response produced by such interactions. The signature comes equipped with a variety of powerful properties rendering it an ideal feature map for streamed data. We summarise recent advances in the symbiosis between deep learning and CDEs, studying the link with RNNs and culminating with the Neural CDE model. We concluded with a discussion on signature kernel methods.
翻译:本文简要概述了在将粗路理论应用于机器学习方面最近取得的一些进展。 控制式差异方程式(CDEs)是用来描述流与物理控制系统相互作用的关键数学模型。 在描述这种相互作用产生的响应时,自然会收集被称为签名的迭代整体体。 签名具有各种强大的特性,使它成为流数据的理想特征图。 我们总结了深层次学习与CDEs之间在共生关系方面的最新进展,研究了与RNS的联系,最后采用了Neural CDE模型。 我们最后讨论了签名内核方法。