• expected signature
• gaussian processes
• time series

The theory of rough paths has gained much attention in the mathematical community since it allows to define a robust theory for controlled differential equation driven by poorly regular signals, such as fractional Brownian motion sample paths.
The concept of signature is strictly related to the theory of rough paths and it has been shown that it is very well suited for machine learning usage.
Indeed, it has been proved that a universal approximation theorem holds and that the expected signature allows to distinguish stochastic processes' law.
In this thesis a new time series classification model that combines gaussian processes and expected signature will be introduced and analyzed.
In particular, the model's forward pass exploits gaussian processes for obtaining a certain number of new time series from a single one, then the expected signature is computed by averaging over each time series's signature and it is used in order to get the output.