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Applications of the theory of rough paths to speech recognition

Final Activity Report Summary - ROUGH (Applications of the theory of rough paths to speech recognition)

Suppose that you are driving a car and you suddenly see an obstacle in front of you. To avoid it, you turn the wheel and press the break. How is the car going to react? The change in the velocity of the car (the 'response' or the 'output') will depend on its current velocity and will be proportional to the changes in the forces that drive the car, caused by the wheel and the break. This is an example of a dynamical system driven by different forces (input). Most 'input - output' or 'driving force - response' systems, either in nature or man-made, can be modelled in this way - we call them dynamical system. But how does the change in the output depend on its current state? Answering this question is vital for making predictions on how a dynamical system will react to a change and can be rather involved, depending on the dimensions or the input and output and the properties of the input.

We have developed a method for estimating the dependence of the change on the current state for a large class of systems, assuming that we know the driving forces. Our method is very general and can tackle situations that have not been considered before: in particular, our method can be applied even when the input is 'rough', i.e. changes very fast (this can be made mathematically precise).