Rough paths, kernels, differential equations and an algebra of functions on streams

Thesis

This thesis is organised in the following four chapters. Appendix A provides asummary of rough path theory.

Chapter 1: Recently, there has been an increased interest in the development of kernel methods for learning with sequential data.The signature kernel is a learning tool with potential to handle irregularly sampled, multivariate time series. In [1] the authors introduced a kernel trick for the truncated version of this kernel avoiding the exponential complexity thatwould hav...

Expand abstract

Authors: Salvi, C

• DOI: 10.5287/ora-ber2ambw1
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Deep learning; Signatures; Time series; Rough paths; Kernels; Differential equations
• Subjects: Machine learning; Stochastic analysis