Rouhgh PathTheory in Machine Learning

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Mohaddes, Ali | 2021

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 54806 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Sharifitabar, Mohsen
Abstract:
In the stochastic analysis, the rough path is a generalization of the concept of smooth paths, which creates a theory for examining the control partial equations arising from irregular signals such as the Wiener process. This theory, which has found wide application in machine learning, time series analysis, and solving stochastic differential equations, is an approach by which the relationship between systems with extreme fluctuations and nonlinear systems is properly expressed.Rough path theory is also interpreted as a generalization of Taylor's expansion for smooth functions. In this research, we try to study the concept of rough path theory and signature and study its various applications in different fields, including machine learning. The signature of a path is a key concept in rough path theory. A path signature is a sequence of repeated integrals that can be used to obtain a non-parametric method for extracting the salient features of data. The data is first converted to multidimensional paths and then used to calculate signatures. This process converts raw information into a set of features used in machine learning
Keywords:
Machine Learning ; Supervised Learning ; Unsupervised Learning ; Stochastic Differential Equation ; Path Signature ; Rough Paths

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