New directions in the applications of rough path theory
It addresses the problem of modeling streamed data interactions for researchers in machine learning and applied mathematics, but is incremental as it provides an overview of existing advances.
The paper reviews recent advances in applying rough path theory and controlled differential equations (CDEs) to machine learning, highlighting the signature as a feature map for streamed data and summarizing developments in deep learning integration, including Neural CDE models and signature kernel methods.
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.